Recursive algorithms are very useful for computing M-estimators of regression coefficients and scatter parameters. In this article, it is shown that for a nondecreasing ul （t）, under some mild conditions the recursi...Recursive algorithms are very useful for computing M-estimators of regression coefficients and scatter parameters. In this article, it is shown that for a nondecreasing ul （t）, under some mild conditions the recursive M-estimators of regression coefficients and scatter parameters are strongly consistent and the recursive M-estimator of the regression coefficients is also asymptotically normal distributed. Furthermore, optimal recursive M-estimators, asymptotic efficiencies of recursive M-estimators and asymptotic relative efficiencies between recursive M-estimators of regression coefficients are studied.展开更多
For nonlinear state estimation driven by non-Gaussian noise,the estimator is required to be updated iteratively.Since the iterative update approximates a linear process,it fails to capture the nonlinearity of observat...For nonlinear state estimation driven by non-Gaussian noise,the estimator is required to be updated iteratively.Since the iterative update approximates a linear process,it fails to capture the nonlinearity of observation models,and this further degrades filtering accuracy and consistency.Given the flaws of nonlinear iteration,this work incorporates a recursive strategy into generalized M-estimation rather than the iterative strategy.The proposed algorithm extends nonlinear recursion to nonlinear systems using the statistical linear regression method.The recursion allows for the gradual release of observation information and consequently enables the update to proceed along the nonlinear direction.Considering the correlated state and observation noise induced by recursions,a separately reweighting strategy is adopted to build a robust nonlinear system.Analogous to the nonlinear recursion,a robust nonlinear recursive update strategy is proposed,where the associated covariances and the observation noise statistics are updated recursively to ensure the consistency of observation noise statistics,thereby completing the nonlinear solution of the robust system.Compared with the iterative update strategies under non-Gaussian observation noise,the recursive update strategy can facilitate the estimator to achieve higher filtering accuracy,stronger robustness,and better consistency.Therefore,the proposed strategy is more suitable for the robust nonlinear filtering framework.展开更多
In this paper,the newly-derived maximum correntropy Kalman filter(MCKF)is re-derived from the M-estimation perspective,where the MCKF can be viewed as a special case of the M-estimations and the Gaussian kernel functi...In this paper,the newly-derived maximum correntropy Kalman filter(MCKF)is re-derived from the M-estimation perspective,where the MCKF can be viewed as a special case of the M-estimations and the Gaussian kernel function is a special case of many robust cost functions.Based on the derivation process,a unified form for the robust Gaussian filters(RGF)based on M-estimation is proposed to suppress the outliers and non-Gaussian noise in the measurement.The RGF provides a unified form for one Gaussian filter with different cost functions and a unified form for one robust filter with different approximating methods for the involved Gaussian integrals.Simulation results show that RGF with different weighting functions and different Gaussian integral approximation methods has robust antijamming performance.展开更多
This paper describes a data reconstruction technique for a multi-function sensor based on the Mestimator, which uses least squares and weighted least squares method. The algorithm has better robustness than convention...This paper describes a data reconstruction technique for a multi-function sensor based on the Mestimator, which uses least squares and weighted least squares method. The algorithm has better robustness than conventional least squares which can amplify the errors of inaccurate data. The M-estimator places particular emphasis on reducing the effects of large data errors, which are further overcome by an iterative regression process which gives small weights to large off-group data errors and large weights to small data errors. Simulation results are consistent with the hypothesis with 81 groups of regression data having an average accuracy of 3.5%, which demonstrates that the M-estimator provides more accurate and reliable data reconstruction.展开更多
In this paper, the moderate deviations for the M-estimators of regression parameter in a linear model are obtained when the errors form a strictly stationary Ф-mixing sequence. The results are applied to study many d...In this paper, the moderate deviations for the M-estimators of regression parameter in a linear model are obtained when the errors form a strictly stationary Ф-mixing sequence. The results are applied to study many different types of M-estimators such as Huber＇s estimator, L^P-regression estimator, least squares estimator and least absolute deviation estimator.展开更多
In this paper, the authors consider an adaptive recursive algorithm by selecting an adaptive sequence for computing M-estimators in multivariate linear regression models. Its asymptotic property is investigated. The r...In this paper, the authors consider an adaptive recursive algorithm by selecting an adaptive sequence for computing M-estimators in multivariate linear regression models. Its asymptotic property is investigated. The recursive algorithm given by Miao and Wu （1996） is modified accordingly. Simu- lation studies of the Mgorithm is also provided. In addition, the Newton-Raphson iterative algorithm is considered for the purpose of comparison.展开更多
The asymptotic behaviour of M-estimalors constructed with B-spline method based on strictly stationary β-mixing observations of a partly linear model is dealt with. Under some regular conditions, it is proved that th...The asymptotic behaviour of M-estimalors constructed with B-spline method based on strictly stationary β-mixing observations of a partly linear model is dealt with. Under some regular conditions, it is proved that the M-estimators of the vector of parameters are asymptotically normal and the M-estimators of the nonparametric component achieve the optimal convergence rates for nonparametric regression. Our asymptotic theory includes L1-, L2-, Lp-norm, and Huber estimators as special cases.展开更多
Under some mild conditions, we establish a strong Bahadur representation of a general class of nonparametric local linear M-estimators for mixing processes on a random field. If the socalled optimal bandwidth hn = O（...Under some mild conditions, we establish a strong Bahadur representation of a general class of nonparametric local linear M-estimators for mixing processes on a random field. If the socalled optimal bandwidth hn = O（｜n｜^-1/5）, n ∈ Z^d, is chosen, then the remainder rates in the Bahadur representation for the local M-estimators of the regression function and its derivative are of order O（｜n｜^-4/5 log ｜n｜）. Moreover, we derive some asymptotic properties for the nonparametric local linear M-estimators as applications of our result.展开更多
Consider the partly linear model K = X1& + go(Ti) + ei, where {(Ti, Xi)}T is a strictlystationary Sequence of random variable8, the ei’8 are i.i.d. random errorsl the K’s are realvalued responsest fo is a &v...Consider the partly linear model K = X1& + go(Ti) + ei, where {(Ti, Xi)}T is a strictlystationary Sequence of random variable8, the ei’8 are i.i.d. random errorsl the K’s are realvalued responsest fo is a &vector of parameters, X is a &vector of explanatory variables,Ti is another explanatory variable ranging over a nondegenerate compact interval. Bnd ona segmnt of observations (T1, Xi 1 Y1 ),’’’ f (Tn, X;, Yn), this article investigates the rates ofconvrgence of the M-estimators for Po and go obtained from the minimisation problemwhere H is a space of B-spline functions of order m + 1 and p(-) is a function chosen suitablyUnder some regularity conditions, it is shown that the estimator of go achieves the optimalglobal rate of convergence of estimators for nonparametric regression, and the estdriator offo is asymptotically normal. The M-estimators here include regression quantile estimators,Li-estimators, Lp-norm estimators, Huber’s type M-estimators and usual least squares estimators. Applications of the asymptotic theory to testing the hypothesis H0: A’β0 =β are alsodiscussed, where β is a given vector and A is a known d × do matrix with rank d0.展开更多
The existing collaborative recommendation algorithms have lower robustness against shilling attacks.With this problem in mind,in this paper we propose a robust collaborative recommendation algorithm based on k-distanc...The existing collaborative recommendation algorithms have lower robustness against shilling attacks.With this problem in mind,in this paper we propose a robust collaborative recommendation algorithm based on k-distance and Tukey M-estimator.Firstly,we propose a k-distancebased method to compute user suspicion degree(USD).The reliable neighbor model can be constructed through incorporating the user suspicion degree into user neighbor model.The influence of attack profiles on the recommendation results is reduced through adjusting similarities among users.Then,Tukey M-estimator is introduced to construct robust matrix factorization model,which can realize the robust estimation of user feature matrix and item feature matrix and reduce the influence of attack profiles on item feature matrix.Finally,a robust collaborative recommendation algorithm is devised by combining the reliable neighbor model and robust matrix factorization model.Experimental results show that the proposed algorithm outperforms the existing methods in terms of both recommendation accuracy and robustness.展开更多
In this paper, to keep scale inveriance, we propose an approximate M-estrmation for the mixed regression model and show consistency of the estimation under weaker conditions than that in [1].
This paper adopts satellite channel brightness temperature simulation to study M-estimator variational retrieval. This approach combines both the advantages of classical variational inversion and robust M-estimators. ...This paper adopts satellite channel brightness temperature simulation to study M-estimator variational retrieval. This approach combines both the advantages of classical variational inversion and robust M-estimators. Classical variational inversion depends on prior quality control to elim- inate outliers, and its errors follow a Gaussian distribution. We coupled the M-estimators to the framework of classical variational inversion to obtain a M-estimator variational inversion. The cost function contains the M-estimator to guarantee the robustness to outliers and improve the retrieval re- sults. The experimental evaluation adopts Feng Yun-3A （FY-3A） simulated data to add to the Gaussian and Non-Gaussian error. The variational in- version is used to obtain the inversion brightness temperature, and temperature and humidity data are used for validation. The preliminary results demonstrate the potential of M-estimator variational retrieval.展开更多
In this paper, by using the Brouwer fixed point theorem, we consider the existence and uniqueness of the solution for local linear regression with variable window breadth.
The vanishing point detection technology helps automatic driving. In this paper, the straight lines on the road associated with the vanishing point are extracted efficiently by using the regional division and angle li...The vanishing point detection technology helps automatic driving. In this paper, the straight lines on the road associated with the vanishing point are extracted efficiently by using the regional division and angle limitation. And, the vanishing point is detected robustly by using the fast M-estimation method. Proposed method could detect straight-line features associated with vanishing point detection efficient on the road. And the vanishing point was detected exactly by the effect of the fast M-estimation method when the straight-line features not associated with vanishing point detection were detected. The processing time of the proposed method was faster than the camera flame rate （30 fps）. Thus, the proposed method is capable of real-time processing.展开更多
In real-world applications, datasets frequently contain outliers, which can hinder the generalization ability of machine learning models. Bayesian classifiers, a popular supervised learning method, rely on accurate pr...In real-world applications, datasets frequently contain outliers, which can hinder the generalization ability of machine learning models. Bayesian classifiers, a popular supervised learning method, rely on accurate probability density estimation for classifying continuous datasets. However, achieving precise density estimation with datasets containing outliers poses a significant challenge. This paper introduces a Bayesian classifier that utilizes optimized robust kernel density estimation to address this issue. Our proposed method enhances the accuracy of probability density distribution estimation by mitigating the impact of outliers on the training sample’s estimated distribution. Unlike the conventional kernel density estimator, our robust estimator can be seen as a weighted kernel mapping summary for each sample. This kernel mapping performs the inner product in the Hilbert space, allowing the kernel density estimation to be considered the average of the samples’ mapping in the Hilbert space using a reproducing kernel. M-estimation techniques are used to obtain accurate mean values and solve the weights. Meanwhile, complete cross-validation is used as the objective function to search for the optimal bandwidth, which impacts the estimator. The Harris Hawks Optimisation optimizes the objective function to improve the estimation accuracy. The experimental results show that it outperforms other optimization algorithms regarding convergence speed and objective function value during the bandwidth search. The optimal robust kernel density estimator achieves better fitness performance than the traditional kernel density estimator when the training data contains outliers. The Naïve Bayesian with optimal robust kernel density estimation improves the generalization in the classification with outliers.展开更多
Maximum likelihood (ML) estimation for the generalized asymmetric Laplace (GAL) distribution also known as Variance gamma using simplex direct search algorithms is investigated. In this paper, we use numerical direct ...Maximum likelihood (ML) estimation for the generalized asymmetric Laplace (GAL) distribution also known as Variance gamma using simplex direct search algorithms is investigated. In this paper, we use numerical direct search techniques for maximizing the log-likelihood to obtain ML estimators instead of using the traditional EM algorithm. The density function of the GAL is only continuous but not differentiable with respect to the parameters and the appearance of the Bessel function in the density make it difficult to obtain the asymptotic covariance matrix for the entire GAL family. Using M-estimation theory, the properties of the ML estimators are investigated in this paper. The ML estimators are shown to be consistent for the GAL family and their asymptotic normality can only be guaranteed for the asymmetric Laplace (AL) family. The asymptotic covariance matrix is obtained for the AL family and it completes the results obtained previously in the literature. For the general GAL model, alternative methods of inferences based on quadratic distances (QD) are proposed. The QD methods appear to be overall more efficient than likelihood methods infinite samples using sample sizes n ≤5000 and the range of parameters often encountered for financial data. The proposed methods only require that the moment generating function of the parametric model exists and has a closed form expression and can be used for other models.展开更多
Asymptotic results are obtained using an approach based on limit theorem results obtained for α-mixing sequences for the class of general spacings (GSP) methods which include the maximum spacings (MSP) method. The MS...Asymptotic results are obtained using an approach based on limit theorem results obtained for α-mixing sequences for the class of general spacings (GSP) methods which include the maximum spacings (MSP) method. The MSP method has been shown to be very useful for estimating parameters for univariate continuous models with a shift at the origin which are often encountered in loss models of actuarial science and extreme models. The MSP estimators have also been shown to be as efficient as maximum likelihood estimators in general and can be used as an alternative method when ML method might have numerical difficulties for some parametric models. Asymptotic properties are presented in a unified way. Robustness results for estimation and parameter testing results which facilitate the applications of the GSP methods are also included and related to quasi-likelihood results.展开更多
Conventional adaptive filtering algorithms often exhibit performance degradation when processing multipath interference in raw echoes of spaceborne synthetic aperture radar(SAR)systems due to anomalous outliers,manife...Conventional adaptive filtering algorithms often exhibit performance degradation when processing multipath interference in raw echoes of spaceborne synthetic aperture radar(SAR)systems due to anomalous outliers,manifesting as insufficient convergence and low estimation accuracy.To address this issue,this study proposes a novel robust adaptive filtering algorithm,namely the M-estimation-based minimum error entropy with affine projection(APMMEE)algorithm.This algorithm inherits the joint multi-data-block update mechanism of the affine projection algorithm,enabling rapid adaptation to the dynamic characteristics of raw echoes and achieving fast convergence.Meanwhile,it incorporates the M-estimation-based minimum error entropy(MMEE)criterion,which weights error samples in raw echoes through M-estimation functions,effectively suppressing outlier interference during the algorithm update.Both the system identification simulations and practical multipath interference suppression experiments using raw echoes demonstrate that the proposed APMMEE algorithm exhibits superior filtering performance.展开更多
基金supported by the Natural Sciences and Engineering Research Council of Canadathe National Natural Science Foundation of China+2 种基金the Doctorial Fund of Education Ministry of Chinasupported by the Natural Sciences and Engineering Research Council of Canadasupported by the National Natural Science Foundation of China
文摘Recursive algorithms are very useful for computing M-estimators of regression coefficients and scatter parameters. In this article, it is shown that for a nondecreasing ul （t）, under some mild conditions the recursive M-estimators of regression coefficients and scatter parameters are strongly consistent and the recursive M-estimator of the regression coefficients is also asymptotically normal distributed. Furthermore, optimal recursive M-estimators, asymptotic efficiencies of recursive M-estimators and asymptotic relative efficiencies between recursive M-estimators of regression coefficients are studied.
基金co-supported by the National Natural Science Foundation of China(No.62303246,No.62103204)the China Postdoctoral Science Foundation(No.2023M731788)。
文摘For nonlinear state estimation driven by non-Gaussian noise,the estimator is required to be updated iteratively.Since the iterative update approximates a linear process,it fails to capture the nonlinearity of observation models,and this further degrades filtering accuracy and consistency.Given the flaws of nonlinear iteration,this work incorporates a recursive strategy into generalized M-estimation rather than the iterative strategy.The proposed algorithm extends nonlinear recursion to nonlinear systems using the statistical linear regression method.The recursion allows for the gradual release of observation information and consequently enables the update to proceed along the nonlinear direction.Considering the correlated state and observation noise induced by recursions,a separately reweighting strategy is adopted to build a robust nonlinear system.Analogous to the nonlinear recursion,a robust nonlinear recursive update strategy is proposed,where the associated covariances and the observation noise statistics are updated recursively to ensure the consistency of observation noise statistics,thereby completing the nonlinear solution of the robust system.Compared with the iterative update strategies under non-Gaussian observation noise,the recursive update strategy can facilitate the estimator to achieve higher filtering accuracy,stronger robustness,and better consistency.Therefore,the proposed strategy is more suitable for the robust nonlinear filtering framework.
基金supported by the Basic Science Center Program of the National Natural Science Foundation of China(62388101)the National Natural Science Foundation of China(61873275).
文摘In this paper,the newly-derived maximum correntropy Kalman filter(MCKF)is re-derived from the M-estimation perspective,where the MCKF can be viewed as a special case of the M-estimations and the Gaussian kernel function is a special case of many robust cost functions.Based on the derivation process,a unified form for the robust Gaussian filters(RGF)based on M-estimation is proposed to suppress the outliers and non-Gaussian noise in the measurement.The RGF provides a unified form for one Gaussian filter with different cost functions and a unified form for one robust filter with different approximating methods for the involved Gaussian integrals.Simulation results show that RGF with different weighting functions and different Gaussian integral approximation methods has robust antijamming performance.
基金the National Natural Science Foundation of China (Nos. 60172071 and 60372005)
文摘This paper describes a data reconstruction technique for a multi-function sensor based on the Mestimator, which uses least squares and weighted least squares method. The algorithm has better robustness than conventional least squares which can amplify the errors of inaccurate data. The M-estimator places particular emphasis on reducing the effects of large data errors, which are further overcome by an iterative regression process which gives small weights to large off-group data errors and large weights to small data errors. Simulation results are consistent with the hypothesis with 81 groups of regression data having an average accuracy of 3.5%, which demonstrates that the M-estimator provides more accurate and reliable data reconstruction.
基金Supported by National Natural Science Foundation of China (Grant Nos. 10871153 and 10971047)
文摘In this paper, the moderate deviations for the M-estimators of regression parameter in a linear model are obtained when the errors form a strictly stationary Ф-mixing sequence. The results are applied to study many different types of M-estimators such as Huber＇s estimator, L^P-regression estimator, least squares estimator and least absolute deviation estimator.
基金supported by the National Natural Science Foundation for Young Scientists of China under Grant No.11101397the Natural Sciences and Engineering Research Council of Canada
文摘In this paper, the authors consider an adaptive recursive algorithm by selecting an adaptive sequence for computing M-estimators in multivariate linear regression models. Its asymptotic property is investigated. The recursive algorithm given by Miao and Wu （1996） is modified accordingly. Simu- lation studies of the Mgorithm is also provided. In addition, the Newton-Raphson iterative algorithm is considered for the purpose of comparison.
基金Project supported in part by the Postdoctoral Science Foundation and the National Natural Science Foundation of China.
文摘The asymptotic behaviour of M-estimalors constructed with B-spline method based on strictly stationary β-mixing observations of a partly linear model is dealt with. Under some regular conditions, it is proved that the M-estimators of the vector of parameters are asymptotically normal and the M-estimators of the nonparametric component achieve the optimal convergence rates for nonparametric regression. Our asymptotic theory includes L1-, L2-, Lp-norm, and Huber estimators as special cases.
基金National Natural Science Foundation of China (No.10771192)
文摘Under some mild conditions, we establish a strong Bahadur representation of a general class of nonparametric local linear M-estimators for mixing processes on a random field. If the socalled optimal bandwidth hn = O（｜n｜^-1/5）, n ∈ Z^d, is chosen, then the remainder rates in the Bahadur representation for the local M-estimators of the regression function and its derivative are of order O（｜n｜^-4/5 log ｜n｜）. Moreover, we derive some asymptotic properties for the nonparametric local linear M-estimators as applications of our result.
文摘Consider the partly linear model K = X1& + go(Ti) + ei, where {(Ti, Xi)}T is a strictlystationary Sequence of random variable8, the ei’8 are i.i.d. random errorsl the K’s are realvalued responsest fo is a &vector of parameters, X is a &vector of explanatory variables,Ti is another explanatory variable ranging over a nondegenerate compact interval. Bnd ona segmnt of observations (T1, Xi 1 Y1 ),’’’ f (Tn, X;, Yn), this article investigates the rates ofconvrgence of the M-estimators for Po and go obtained from the minimisation problemwhere H is a space of B-spline functions of order m + 1 and p(-) is a function chosen suitablyUnder some regularity conditions, it is shown that the estimator of go achieves the optimalglobal rate of convergence of estimators for nonparametric regression, and the estdriator offo is asymptotically normal. The M-estimators here include regression quantile estimators,Li-estimators, Lp-norm estimators, Huber’s type M-estimators and usual least squares estimators. Applications of the asymptotic theory to testing the hypothesis H0: A’β0 =β are alsodiscussed, where β is a given vector and A is a known d × do matrix with rank d0.
基金National Natural Science Foundation of China under Grant No.61379116，Natural Science Foundation of Hebei Province under Grant No.F2015203046 and No.F2013203124，Key Program of Research on Science and Technology of Higher Education Institutions of Hebei Province under Grant No.ZH2012028
文摘The existing collaborative recommendation algorithms have lower robustness against shilling attacks.With this problem in mind,in this paper we propose a robust collaborative recommendation algorithm based on k-distance and Tukey M-estimator.Firstly,we propose a k-distancebased method to compute user suspicion degree(USD).The reliable neighbor model can be constructed through incorporating the user suspicion degree into user neighbor model.The influence of attack profiles on the recommendation results is reduced through adjusting similarities among users.Then,Tukey M-estimator is introduced to construct robust matrix factorization model,which can realize the robust estimation of user feature matrix and item feature matrix and reduce the influence of attack profiles on item feature matrix.Finally,a robust collaborative recommendation algorithm is devised by combining the reliable neighbor model and robust matrix factorization model.Experimental results show that the proposed algorithm outperforms the existing methods in terms of both recommendation accuracy and robustness.
文摘In this paper, to keep scale inveriance, we propose an approximate M-estrmation for the mixed regression model and show consistency of the estimation under weaker conditions than that in [1].
基金Supported by Special Scientific Research Fund of Meteorological Public Welfare Profession of China(GYHY201406028)Meteorological Open Research Fund for Huaihe River Basin(HRM201407)Anhui Meteorological Bureau Science and Technology Development Fund(RC201506)
文摘This paper adopts satellite channel brightness temperature simulation to study M-estimator variational retrieval. This approach combines both the advantages of classical variational inversion and robust M-estimators. Classical variational inversion depends on prior quality control to elim- inate outliers, and its errors follow a Gaussian distribution. We coupled the M-estimators to the framework of classical variational inversion to obtain a M-estimator variational inversion. The cost function contains the M-estimator to guarantee the robustness to outliers and improve the retrieval re- sults. The experimental evaluation adopts Feng Yun-3A （FY-3A） simulated data to add to the Gaussian and Non-Gaussian error. The variational in- version is used to obtain the inversion brightness temperature, and temperature and humidity data are used for validation. The preliminary results demonstrate the potential of M-estimator variational retrieval.
文摘In this paper, by using the Brouwer fixed point theorem, we consider the existence and uniqueness of the solution for local linear regression with variable window breadth.
文摘The vanishing point detection technology helps automatic driving. In this paper, the straight lines on the road associated with the vanishing point are extracted efficiently by using the regional division and angle limitation. And, the vanishing point is detected robustly by using the fast M-estimation method. Proposed method could detect straight-line features associated with vanishing point detection efficient on the road. And the vanishing point was detected exactly by the effect of the fast M-estimation method when the straight-line features not associated with vanishing point detection were detected. The processing time of the proposed method was faster than the camera flame rate （30 fps）. Thus, the proposed method is capable of real-time processing.
文摘In real-world applications, datasets frequently contain outliers, which can hinder the generalization ability of machine learning models. Bayesian classifiers, a popular supervised learning method, rely on accurate probability density estimation for classifying continuous datasets. However, achieving precise density estimation with datasets containing outliers poses a significant challenge. This paper introduces a Bayesian classifier that utilizes optimized robust kernel density estimation to address this issue. Our proposed method enhances the accuracy of probability density distribution estimation by mitigating the impact of outliers on the training sample’s estimated distribution. Unlike the conventional kernel density estimator, our robust estimator can be seen as a weighted kernel mapping summary for each sample. This kernel mapping performs the inner product in the Hilbert space, allowing the kernel density estimation to be considered the average of the samples’ mapping in the Hilbert space using a reproducing kernel. M-estimation techniques are used to obtain accurate mean values and solve the weights. Meanwhile, complete cross-validation is used as the objective function to search for the optimal bandwidth, which impacts the estimator. The Harris Hawks Optimisation optimizes the objective function to improve the estimation accuracy. The experimental results show that it outperforms other optimization algorithms regarding convergence speed and objective function value during the bandwidth search. The optimal robust kernel density estimator achieves better fitness performance than the traditional kernel density estimator when the training data contains outliers. The Naïve Bayesian with optimal robust kernel density estimation improves the generalization in the classification with outliers.
文摘Maximum likelihood (ML) estimation for the generalized asymmetric Laplace (GAL) distribution also known as Variance gamma using simplex direct search algorithms is investigated. In this paper, we use numerical direct search techniques for maximizing the log-likelihood to obtain ML estimators instead of using the traditional EM algorithm. The density function of the GAL is only continuous but not differentiable with respect to the parameters and the appearance of the Bessel function in the density make it difficult to obtain the asymptotic covariance matrix for the entire GAL family. Using M-estimation theory, the properties of the ML estimators are investigated in this paper. The ML estimators are shown to be consistent for the GAL family and their asymptotic normality can only be guaranteed for the asymmetric Laplace (AL) family. The asymptotic covariance matrix is obtained for the AL family and it completes the results obtained previously in the literature. For the general GAL model, alternative methods of inferences based on quadratic distances (QD) are proposed. The QD methods appear to be overall more efficient than likelihood methods infinite samples using sample sizes n ≤5000 and the range of parameters often encountered for financial data. The proposed methods only require that the moment generating function of the parametric model exists and has a closed form expression and can be used for other models.
文摘Asymptotic results are obtained using an approach based on limit theorem results obtained for α-mixing sequences for the class of general spacings (GSP) methods which include the maximum spacings (MSP) method. The MSP method has been shown to be very useful for estimating parameters for univariate continuous models with a shift at the origin which are often encountered in loss models of actuarial science and extreme models. The MSP estimators have also been shown to be as efficient as maximum likelihood estimators in general and can be used as an alternative method when ML method might have numerical difficulties for some parametric models. Asymptotic properties are presented in a unified way. Robustness results for estimation and parameter testing results which facilitate the applications of the GSP methods are also included and related to quasi-likelihood results.
基金supported by Shandong Provincial Natural Science Foundation(No.ZR2022MF314).
文摘Conventional adaptive filtering algorithms often exhibit performance degradation when processing multipath interference in raw echoes of spaceborne synthetic aperture radar(SAR)systems due to anomalous outliers,manifesting as insufficient convergence and low estimation accuracy.To address this issue,this study proposes a novel robust adaptive filtering algorithm,namely the M-estimation-based minimum error entropy with affine projection(APMMEE)algorithm.This algorithm inherits the joint multi-data-block update mechanism of the affine projection algorithm,enabling rapid adaptation to the dynamic characteristics of raw echoes and achieving fast convergence.Meanwhile,it incorporates the M-estimation-based minimum error entropy(MMEE)criterion,which weights error samples in raw echoes through M-estimation functions,effectively suppressing outlier interference during the algorithm update.Both the system identification simulations and practical multipath interference suppression experiments using raw echoes demonstrate that the proposed APMMEE algorithm exhibits superior filtering performance.
