Because the real input acceleration cannot be obtained during the error model identification of inertial navigation platform, both the input and output data contain noises. In this case, the conventional regression mo...Because the real input acceleration cannot be obtained during the error model identification of inertial navigation platform, both the input and output data contain noises. In this case, the conventional regression model and the least squares （LS） method will result in bias. Based on the models of inertial navigation platform error and observation error, the errors-in-variables （EV） model and the total least squares （TLS） method axe proposed to identify the error model of the inertial navigation platform. The estimation precision is improved and the result is better than the conventional regression model based LS method. The simulation results illustrate the effectiveness of the proposed method.展开更多
This paper proposes a novel method to quantify the error of a nominal normalized right graph symbol （NRGS） for an errors- in-variables （EIV） system corrupted with bounded noise. Following an identification framewo...This paper proposes a novel method to quantify the error of a nominal normalized right graph symbol （NRGS） for an errors- in-variables （EIV） system corrupted with bounded noise. Following an identification framework for estimation of a perturbation model set, a worst-case v-gap error bound for the estimated nominal NRGS can be first determined from a priori and a posteriori information on the underlying EIV system. Then, an NRGS perturbation model set can be derived from a close relation between the v-gap metric of two models and H∞-norm of their NRGSs＇ difference. The obtained NRGS perturbation model set paves the way for robust controller design using an H∞ loop-shaping method because it is a standard form of the well-known NCF （normalized coprime factor） perturbation model set. Finally, a numerical simulation is used to demonstrate the effectiveness of the proposed identification method.展开更多
We study the subspace identification for the continuous-time errors-in-variables model from sampled data.First,the filtering approach is applied to handle the time-derivative problem inherent in continuous-time identi...We study the subspace identification for the continuous-time errors-in-variables model from sampled data.First,the filtering approach is applied to handle the time-derivative problem inherent in continuous-time identification.The generalized Poisson moment functional is focused.A total least squares equation based on this filtering approach is derived.Inspired by the idea of discrete-time subspace identification based on principal component analysis,we develop two algorithms to deliver consistent estimates for the continuous-time errors-in-variables model by introducing two different instrumental variables.Order determination and other instrumental variables are discussed.The usefulness of the proposed algorithms is illustrated through numerical simulation.展开更多
The reliability theory has been an important element of the classical geodetic adjustment theory and methods in the linear Gauss-Markov model. Although errors-in-variables(EIV) models have been intensively investigate...The reliability theory has been an important element of the classical geodetic adjustment theory and methods in the linear Gauss-Markov model. Although errors-in-variables(EIV) models have been intensively investigated, little has been done about reliability theory for EIV models. This paper first investigates the effect of a random coefficient matrix A on the conventional geodetic reliability measures as if the coefficient matrix were deterministic. The effects of such geodetic internal and external reliability measures due to the randomness of the coefficient matrix are worked out, which are shown to depend not only on the noise level of the random elements of A but also on the values of parameters. An alternative, linear approximate reliability theory is accordingly developed for use in EIV models. Both the EIV-affected reliability measures and the corresponding linear approximate measures fully account for the random errors of both the coefficient matrix and the observations, though formulated in a slightly different way. Numerical experiments have been carried to demonstrate the effects of errors-in-variables on reliability measures and compared with the conventional Baarda's reliability measures. The simulations have confirmed our theoretical results that the EIV-reliability measures depend on both the noise level of A and the parameter values. The larger the noise level of A, the larger the EIV-affected internal and external reliability measures;the larger the parameters,the larger the EIV-affected internal and external reliability measures.展开更多
The FRF estimator based on the errors-in-variables （EV） model of multi-input multi-output （MIMO） system is presented to reduce the bias error of FRF HI estimator. The FRF HI estimator is influenced by the noises i...The FRF estimator based on the errors-in-variables （EV） model of multi-input multi-output （MIMO） system is presented to reduce the bias error of FRF HI estimator. The FRF HI estimator is influenced by the noises in the inputs of the system and generates an under-estimation of the true FRF. The FRF estimator based on the EV model takes into account the errors in both the inputs and outputs of the system and would lead to more accurate FRF estimation. The FRF estimator based on the EV model is applied to the waveform replication on the 6-DOF （degree-of-freedom） hydraulic vibration table. The result shows that it is favorable to improve the control precision of the MIMO vibration control system.展开更多
Estimators are presented for the coefficients of the polynomial errors-in-variables (EV) model when replicated observations are taken at some experimental points. These estimators are shown to be strongly consistent u...Estimators are presented for the coefficients of the polynomial errors-in-variables (EV) model when replicated observations are taken at some experimental points. These estimators are shown to be strongly consistent under mild conditions.展开更多
This paper concerns the identification problem of scalar errors-in-variables(EIV)systems with general nonlinear output observations and ARMA observation noises.Under independent and identically distributed(i.i.d.)Gaus...This paper concerns the identification problem of scalar errors-in-variables(EIV)systems with general nonlinear output observations and ARMA observation noises.Under independent and identically distributed(i.i.d.)Gaussian inputs with unknown variance,recursive algorithms for estimating the parameters of the EIV systems are presented.For general nonlinear observations,conditions on the system are imposed to guarantee the almost sure convergence of the estimates.A simulation example is included to justify the theoretical results.展开更多
This paper discusses robust nonparametric estimators of location regression function for errorsin-variables model with de-convolution kernel.The local constant smoother is used for the estimation of the nonparametric ...This paper discusses robust nonparametric estimators of location regression function for errorsin-variables model with de-convolution kernel.The local constant smoother is used for the estimation of the nonparametric function,and the local linear smoother is proposed to deal with the boundary problem,as well as to improve the local constant smoother.We establish the asymptotic properties of the estimator,the influence function of the statistical functional and the breakdown point.A simulation study is carried out to demonstrate robust performance of the proposed estimator.The motorcycle data is presented to illustrate the application of the robust estimator further.展开更多
While the random errors are a function of Gaussian random variables that are stationary and long dependent, we investigate a partially linear errors-in-variables（EV） model by the wavelet method. Under general condit...While the random errors are a function of Gaussian random variables that are stationary and long dependent, we investigate a partially linear errors-in-variables（EV） model by the wavelet method. Under general conditions, we obtain asymptotic representation of the parametric estimator, and asymptotic distributions and weak convergence rates of the parametric and nonparametric estimators. At last, the validity of the wavelet method is illuminated by a simulation example and a real example.展开更多
In this paper, we consider the partially nonlinear errors-in-variables models when the non- parametric component is measured with additive error. The profile nonlinear least squares estimator of unknown parameter and ...In this paper, we consider the partially nonlinear errors-in-variables models when the non- parametric component is measured with additive error. The profile nonlinear least squares estimator of unknown parameter and the estimator of nonparametric component are constructed, and their asymptotic properties are derived under general assumptions. Finite sample performances of the proposed statistical inference procedures are illustrated by Monte Carlo simulation studies.展开更多
This paper proposes a new approach for variable selection in partially linear errors-in-variables （EV） models for longitudinal data by penalizing appropriate estimating functions. We apply the SCAD penalty to simult...This paper proposes a new approach for variable selection in partially linear errors-in-variables （EV） models for longitudinal data by penalizing appropriate estimating functions. We apply the SCAD penalty to simultaneously select significant variables and estimate unknown parameters. The rate of convergence and the asymptotic normality of the resulting estimators are established. Furthermore, with proper choice of regularization parameters, we show that the proposed estimators perform as well as the oracle procedure. A new algorithm is proposed for solving penalized estimating equation. The asymptotic results are augmented by a simulation study.展开更多
A kind of partially linear errors-in-variables models with replicated net points of observation are studied in this paper. Estimators of unknown parameters are given. Under certain regular conditions, it is shown that...A kind of partially linear errors-in-variables models with replicated net points of observation are studied in this paper. Estimators of unknown parameters are given. Under certain regular conditions, it is shown that the estimators of the unknown parameters are strongly consistent and their a.s. convergence rates are achieved.展开更多
The authors consider the partially linear model relating a response Y to predictors （x, T） with a mean function x^Tβ0 ＋ g（T） when the x＇s are measured with an additive error. The estimators of parameter β0 are...The authors consider the partially linear model relating a response Y to predictors （x, T） with a mean function x^Tβ0 ＋ g（T） when the x＇s are measured with an additive error. The estimators of parameter β0 are derived by using the nearest neighbor-generalized randomly weighted least absolute deviation （LAD for short） method. The resulting estimator of the unknown vector 30 is shown to be consistent and asymptotically normal. In addition, the results facilitate the construction of confidence regions and the hypothesis testing for the unknown parameters. Extensive simulations are reported, showing that the proposed method works well in practical settings. The proposed methods are also applied to a data set from the study of an AIDS clinical trial group.展开更多
This paper studies the parameter estimation of multiple dimensional linear errors-in-variables (EV) models in the case where replicated observations are available in some experimental points. Asymptotic normality is e...This paper studies the parameter estimation of multiple dimensional linear errors-in-variables (EV) models in the case where replicated observations are available in some experimental points. Asymptotic normality is established under mild conditions, and the parameters entering the asymptotic variance are consistently estimated to render the result useable in the construction of large-sample confidence regions.展开更多
When a regression model is applied as an approximation of underlying model of data, the model checking is important and relevant. In this paper, we investigate the lack-of-fit test for a polynomial errorin-variables m...When a regression model is applied as an approximation of underlying model of data, the model checking is important and relevant. In this paper, we investigate the lack-of-fit test for a polynomial errorin-variables model. As the ordinary residuals are biased when there exist measurement errors in covariables, we correct them and then construct a residual-based test of score type. The constructed test is asymptotically chi-squared under null hypotheses. Simulation study shows that the test can maintain the signi.cance level well. The choice of weight functions involved in the test statistic and the related power study are also investigated. The application to two examples is illustrated. The approach can be readily extended to handle more general models.展开更多
基金supported by the National Security Major Basic Research Project of China (973-61334).
文摘Because the real input acceleration cannot be obtained during the error model identification of inertial navigation platform, both the input and output data contain noises. In this case, the conventional regression model and the least squares （LS） method will result in bias. Based on the models of inertial navigation platform error and observation error, the errors-in-variables （EV） model and the total least squares （TLS） method axe proposed to identify the error model of the inertial navigation platform. The estimation precision is improved and the result is better than the conventional regression model based LS method. The simulation results illustrate the effectiveness of the proposed method.
基金supported in part by the National Natural Science Foundation of China(Nos.61203119,61304153)the Key Program of Tianjin Natural Science Foundation,China(No.14JCZDJC36300)the Tianjin University of Technology and Education funded project(No.RC14-48)
文摘This paper proposes a novel method to quantify the error of a nominal normalized right graph symbol （NRGS） for an errors- in-variables （EIV） system corrupted with bounded noise. Following an identification framework for estimation of a perturbation model set, a worst-case v-gap error bound for the estimated nominal NRGS can be first determined from a priori and a posteriori information on the underlying EIV system. Then, an NRGS perturbation model set can be derived from a close relation between the v-gap metric of two models and H∞-norm of their NRGSs＇ difference. The obtained NRGS perturbation model set paves the way for robust controller design using an H∞ loop-shaping method because it is a standard form of the well-known NCF （normalized coprime factor） perturbation model set. Finally, a numerical simulation is used to demonstrate the effectiveness of the proposed identification method.
基金supported by the National Natural Science Foundation of China (Nos.60674086 and 60736021)the Scientific and Technology Plan of Zhejiang Province,China (No.2007C21173)
文摘We study the subspace identification for the continuous-time errors-in-variables model from sampled data.First,the filtering approach is applied to handle the time-derivative problem inherent in continuous-time identification.The generalized Poisson moment functional is focused.A total least squares equation based on this filtering approach is derived.Inspired by the idea of discrete-time subspace identification based on principal component analysis,we develop two algorithms to deliver consistent estimates for the continuous-time errors-in-variables model by introducing two different instrumental variables.Order determination and other instrumental variables are discussed.The usefulness of the proposed algorithms is illustrated through numerical simulation.
基金supported by the National Natural Science Foundation of China, Project No. 42174045under National Key Research and Development Program of China, Project No.2020YFB0505805the National Natural Science Foundation of China, Project No. 41874012。
文摘The reliability theory has been an important element of the classical geodetic adjustment theory and methods in the linear Gauss-Markov model. Although errors-in-variables(EIV) models have been intensively investigated, little has been done about reliability theory for EIV models. This paper first investigates the effect of a random coefficient matrix A on the conventional geodetic reliability measures as if the coefficient matrix were deterministic. The effects of such geodetic internal and external reliability measures due to the randomness of the coefficient matrix are worked out, which are shown to depend not only on the noise level of the random elements of A but also on the values of parameters. An alternative, linear approximate reliability theory is accordingly developed for use in EIV models. Both the EIV-affected reliability measures and the corresponding linear approximate measures fully account for the random errors of both the coefficient matrix and the observations, though formulated in a slightly different way. Numerical experiments have been carried to demonstrate the effects of errors-in-variables on reliability measures and compared with the conventional Baarda's reliability measures. The simulations have confirmed our theoretical results that the EIV-reliability measures depend on both the noise level of A and the parameter values. The larger the noise level of A, the larger the EIV-affected internal and external reliability measures;the larger the parameters,the larger the EIV-affected internal and external reliability measures.
基金This project is supported by Program for New Century Excellent Talents in University,China(No.NCET-04-0325).
文摘The FRF estimator based on the errors-in-variables （EV） model of multi-input multi-output （MIMO） system is presented to reduce the bias error of FRF HI estimator. The FRF HI estimator is influenced by the noises in the inputs of the system and generates an under-estimation of the true FRF. The FRF estimator based on the EV model takes into account the errors in both the inputs and outputs of the system and would lead to more accurate FRF estimation. The FRF estimator based on the EV model is applied to the waveform replication on the 6-DOF （degree-of-freedom） hydraulic vibration table. The result shows that it is favorable to improve the control precision of the MIMO vibration control system.
基金This work was supported by the National Natural Science Foundation of China (Grant No.19631040).
文摘Estimators are presented for the coefficients of the polynomial errors-in-variables (EV) model when replicated observations are taken at some experimental points. These estimators are shown to be strongly consistent under mild conditions.
基金supported by the National Natural Science Foundation of China under Grant No.11571362.
文摘This paper concerns the identification problem of scalar errors-in-variables(EIV)systems with general nonlinear output observations and ARMA observation noises.Under independent and identically distributed(i.i.d.)Gaussian inputs with unknown variance,recursive algorithms for estimating the parameters of the EIV systems are presented.For general nonlinear observations,conditions on the system are imposed to guarantee the almost sure convergence of the estimates.A simulation example is included to justify the theoretical results.
基金partly supported by the National Natural Science Foundation of China(Grant Nos.1971324,11471223)Capacity Building for Sci-Tech Innovation-Fundamental Scientific Research Funds(No:19530050181)Interdiscipline for Bioinformatics and Statistics and Academy for Multidisciplinary Studies of Capital Normal University,Beijing.
文摘This paper discusses robust nonparametric estimators of location regression function for errorsin-variables model with de-convolution kernel.The local constant smoother is used for the estimation of the nonparametric function,and the local linear smoother is proposed to deal with the boundary problem,as well as to improve the local constant smoother.We establish the asymptotic properties of the estimator,the influence function of the statistical functional and the breakdown point.A simulation study is carried out to demonstrate robust performance of the proposed estimator.The motorcycle data is presented to illustrate the application of the robust estimator further.
基金Supported by the National Natural Science Foundation of China(No.11471105,11471223)Scientific Research Item of Education Office,Hubei(No.D20172501)
文摘While the random errors are a function of Gaussian random variables that are stationary and long dependent, we investigate a partially linear errors-in-variables（EV） model by the wavelet method. Under general conditions, we obtain asymptotic representation of the parametric estimator, and asymptotic distributions and weak convergence rates of the parametric and nonparametric estimators. At last, the validity of the wavelet method is illuminated by a simulation example and a real example.
基金Supported by National Natural Science Foundation of China(Grant Nos.11101014 and 11002005)the Beijing Natural Science Foundation(Grant No.1142002)+2 种基金the Doctoral Fund of Innovation of Beijing Universityof Technologythe Science and Technology Project of Beijing Municipal Education Commission(Grant No.KM201410005010)the Training Programme Foundation for the Beijing Municipal Excellent Talents(GrantNo.2013D005007000005)
文摘In this paper, we consider the partially nonlinear errors-in-variables models when the non- parametric component is measured with additive error. The profile nonlinear least squares estimator of unknown parameter and the estimator of nonparametric component are constructed, and their asymptotic properties are derived under general assumptions. Finite sample performances of the proposed statistical inference procedures are illustrated by Monte Carlo simulation studies.
基金Supported by the National Natural Science Foundation of China (Nos.11126332 and 11101452)the National Social Science Foundation of China (No.11CTJ004)+1 种基金the Natural Science Foundation Project of CQ CSTC(No.cstc2011jjA00014)the Research Foundation of Chongqing Municipal Education Commission (No.KJ110720)
文摘This paper proposes a new approach for variable selection in partially linear errors-in-variables （EV） models for longitudinal data by penalizing appropriate estimating functions. We apply the SCAD penalty to simultaneously select significant variables and estimate unknown parameters. The rate of convergence and the asymptotic normality of the resulting estimators are established. Furthermore, with proper choice of regularization parameters, we show that the proposed estimators perform as well as the oracle procedure. A new algorithm is proposed for solving penalized estimating equation. The asymptotic results are augmented by a simulation study.
基金Supported by the National Natural Science Foundation of China(No.90104034,No.60373041).
文摘A kind of partially linear errors-in-variables models with replicated net points of observation are studied in this paper. Estimators of unknown parameters are given. Under certain regular conditions, it is shown that the estimators of the unknown parameters are strongly consistent and their a.s. convergence rates are achieved.
文摘The authors consider the partially linear model relating a response Y to predictors （x, T） with a mean function x^Tβ0 ＋ g（T） when the x＇s are measured with an additive error. The estimators of parameter β0 are derived by using the nearest neighbor-generalized randomly weighted least absolute deviation （LAD for short） method. The resulting estimator of the unknown vector 30 is shown to be consistent and asymptotically normal. In addition, the results facilitate the construction of confidence regions and the hypothesis testing for the unknown parameters. Extensive simulations are reported, showing that the proposed method works well in practical settings. The proposed methods are also applied to a data set from the study of an AIDS clinical trial group.
基金This project is supported by the National Natural Science Foundation of China (No.19631040)
文摘This paper studies the parameter estimation of multiple dimensional linear errors-in-variables (EV) models in the case where replicated observations are available in some experimental points. Asymptotic normality is established under mild conditions, and the parameters entering the asymptotic variance are consistently estimated to render the result useable in the construction of large-sample confidence regions.
基金a CRCG Grant of the University of Hong Kong and a RGC Grant of Hong Kong,HKSAR,ChinaNational Natural Science Foundation of China (No.10071009).
文摘When a regression model is applied as an approximation of underlying model of data, the model checking is important and relevant. In this paper, we investigate the lack-of-fit test for a polynomial errorin-variables model. As the ordinary residuals are biased when there exist measurement errors in covariables, we correct them and then construct a residual-based test of score type. The constructed test is asymptotically chi-squared under null hypotheses. Simulation study shows that the test can maintain the signi.cance level well. The choice of weight functions involved in the test statistic and the related power study are also investigated. The application to two examples is illustrated. The approach can be readily extended to handle more general models.
