In this study, a multivariate local quadratic polynomial regression(MLQPR) method is proposed to design a model for the sludge volume index(SVI). In MLQPR, a quadratic polynomial regression function is established to ...In this study, a multivariate local quadratic polynomial regression(MLQPR) method is proposed to design a model for the sludge volume index(SVI). In MLQPR, a quadratic polynomial regression function is established to describe the relationship between SVI and the relative variables, and the important terms of the quadratic polynomial regression function are determined by the significant test of the corresponding coefficients. Moreover, a local estimation method is introduced to adjust the weights of the quadratic polynomial regression function to improve the model accuracy. Finally, the proposed method is applied to predict the SVI values in a real wastewater treatment process(WWTP). The experimental results demonstrate that the proposed MLQPR method has faster testing speed and more accurate results than some existing methods.展开更多
In this article, authors introduce a method to assess local influence of obser- vations on the parameter estimates and prediction in multivariate regression model. The diagnostics under the perturbations of error vari...In this article, authors introduce a method to assess local influence of obser- vations on the parameter estimates and prediction in multivariate regression model. The diagnostics under the perturbations of error variance, response variables and explanatory variables are derived, and the results are compared with those of case- deletion. Two examples are analyzed for illustration.展开更多
In this paper, we try to find numerical solution of y'(x)= p(x)y(x)+g(x)+λ∫ba K(x, t)y(t)dt, y(a)=α. a≤x≤b, a≤t≤b or y'(x)= p(x)y(x)+g(x)+λ∫xa K(x, t)y(t)dt, y(a)=α. a≤x≤b, a≤t≤b by using Local p...In this paper, we try to find numerical solution of y'(x)= p(x)y(x)+g(x)+λ∫ba K(x, t)y(t)dt, y(a)=α. a≤x≤b, a≤t≤b or y'(x)= p(x)y(x)+g(x)+λ∫xa K(x, t)y(t)dt, y(a)=α. a≤x≤b, a≤t≤b by using Local polynomial regression (LPR) method. The numerical solution shows that this method is powerful in solving integro-differential equations. The method will be tested on three model problems in order to demonstrate its usefulness and accuracy.展开更多
Global statistical techniques often assume homogeneity of relationships between dependent variable and predictors across space. This assumption has been criticized by statistical geographers as a fundamental weakness ...Global statistical techniques often assume homogeneity of relationships between dependent variable and predictors across space. This assumption has been criticized by statistical geographers as a fundamental weakness that may yield misleading result when it is applied to dataset with spatial context. To strengthen this weakness, a new method that accounts for heterogeneity in relationships across geographic space has been presented. This is one of the family of local spatial statistical techniques referred to as geographically weighted regression (GWR). The method captures non-stationarity of relationship in spatial data that the ordinary least square (OLS) regression fails to account for. Thus, the paper is designed to explore and analyze the spatial relationships between cholera occurrence and household sources of water supply using GIS-based GWR, also to compare the modeling fitness of OLS and GWR. Vector dataset (spatial) of the study region by state levels and statistical data (non-spatial) on cholera cases, household sources of water supply and population data were used in this exploratory analysis. The result shows that GWR is a significant improvement on the global model. Comparing both models with the AICc value and the R2 value revealed that for the former, the value is reduced from 698.7 (for OLS model) to 691.5 (for GWR model). For the latter, OLS explained 66.4 percent while GWR explained 86.7 percent. This implies that local model’s fitness is higher than global model. In addition, the empirical analysis revealed that cholera occurrence in the study region is significantly associated with household sources of water supply. This relationship, as detected by GWR, largely varies across the region.展开更多
This paper proposes parametric component and nonparametric component estimators in a semiparametric regression models based on least squares and weight function's method, their strong consistency and rib mean cons...This paper proposes parametric component and nonparametric component estimators in a semiparametric regression models based on least squares and weight function's method, their strong consistency and rib mean consistency are obtained under a locally generallied Gaussinan error's structure. Finally, the author showes that the usual weight functions based on nearest neighbor method satisfy the deigned assumptions imposed.展开更多
The magnetic information measured on the smartphone platform has a large fluctuation and the research of indoor localization algorithm based on smart-phone platform is less. Indoor localization algorithm on smartphone...The magnetic information measured on the smartphone platform has a large fluctuation and the research of indoor localization algorithm based on smart-phone platform is less. Indoor localization algorithm on smartphone platform based on particle filter is studied. Robust local weighted regression is used to smooth the original magnetic data in the process of constructing magnetic map. Use moving average filtering model to filter the online magnetic observation data in positioning process. Compare processed online magnetic data with processed magnetic map collected by smartphone platform and the average matching error is 0.3941uT. Average positioning error is 0.229 meter when using processed online and map data.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.
In this paper, auxiliary information is used to determine an estimator of finite population total using nonparametric regression under stratified random sampling. To achieve this, a model-based approach is adopted by ...In this paper, auxiliary information is used to determine an estimator of finite population total using nonparametric regression under stratified random sampling. To achieve this, a model-based approach is adopted by making use of the local polynomial regression estimation to predict the nonsampled values of the survey variable y. The performance of the proposed estimator is investigated against some design-based and model-based regression estimators. The simulation experiments show that the resulting estimator exhibits good properties. Generally, good confidence intervals are seen for the nonparametric regression estimators, and use of the proposed estimator leads to relatively smaller values of RE compared to other estimators.展开更多
In this paper, an overview of an important feature in statistics field has shown： the stepwise multiple linear regression. Likewise, a link between stepwise multiple linear regression and earthquakes localization has...In this paper, an overview of an important feature in statistics field has shown： the stepwise multiple linear regression. Likewise, a link between stepwise multiple linear regression and earthquakes localization has been descripted. Precisely, the aim of this research is showing how stepwise multiple linear regression contributes to solution of earthquakes localization, describing its conditions of use in HYPO71PC, a software devoted to computation of seismic sources’ collocation. This aim is reached treating a concrete case, that is computation of earthquakes localization happening on Mount Vesuvius, Italy.展开更多
There are a variety of classification techniques such as neural network, decision tree, support vector machine and logistic regression. The problem of dimensionality is pertinent to many learning algorithms, and it de...There are a variety of classification techniques such as neural network, decision tree, support vector machine and logistic regression. The problem of dimensionality is pertinent to many learning algorithms, and it denotes the drastic raise of computational complexity, however, we need to use dimensionality reduction methods. These methods include principal component analysis (PCA) and locality preserving projection (LPP). In many real-world classification problems, the local structure is more important than the global structure and dimensionality reduction techniques ignore the local structure and preserve the global structure. The objectives is to compare PCA and LPP in terms of accuracy, to develop appropriate representations of complex data by reducing the dimensions of the data and to explain the importance of using LPP with logistic regression. The results of this paper find that the proposed LPP approach provides a better representation and high accuracy than the PCA approach.展开更多
In this paper,a class of functional-coefficient regression models is proposed and an estimation procedure based on the locally weighted least equares is suggested.This class of models,with the proposed estimation meth...In this paper,a class of functional-coefficient regression models is proposed and an estimation procedure based on the locally weighted least equares is suggested.This class of models,with the proposed estimation method,is a powerful means for exploratory data analysis.展开更多
In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the l...In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the local linear technique and the averaged method,the initial estimates of the coefficient functions are given.Second step,based on the initial estimates,the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure.The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions.Two simulated examples show that the procedure is effective.展开更多
In order to improve classification accuracy, the regularized logistic regression is used to classify single-trial electroencephalogram （EEG）. A novel approach, named local sparse logistic regression （LSLR）, is pro...In order to improve classification accuracy, the regularized logistic regression is used to classify single-trial electroencephalogram （EEG）. A novel approach, named local sparse logistic regression （LSLR）, is proposed. The LSLR integrates the locality preserving projection regularization term into the framework of sparse logistic regression. It tries to maintain the neighborhood information of original feature space, and, meanwhile, keeps sparsity. The bound optimization algorithm and component-wise update are used to compute the weight vector in the training data, thus overcoming the disadvantage of the Newton-Raphson method and iterative re-weighted least squares （IRLS）. The classification accuracy of 80% is achieved using ten-fold cross-validation in the self-paced finger tapping data set. The results of LSLR are compared with SLR, showing the effectiveness of the proposed method.展开更多
This study used spatial autoregression(SAR)model and geographically weighted regression(GWR)model to model the spatial patterns of farmland density and its temporal change in Gucheng County,Hubei Province,China in 199...This study used spatial autoregression(SAR)model and geographically weighted regression(GWR)model to model the spatial patterns of farmland density and its temporal change in Gucheng County,Hubei Province,China in 1999 and 2009,and discussed the difference between global and local spatial autocorrelations in terms of spatial heterogeneity and non-stationarity.Results showed that strong spatial positive correlations existed in the spatial distributions of farmland density,its temporal change and the driving factors,and the coefficients of spatial autocorrelations decreased as the spatial lag distance increased.SAR models revealed the global spatial relations between dependent and independent variables,while the GWR model showed the spatially varying fitting degree and local weighting coefficients of driving factors and farmland indices(i.e.,farmland density and temporal change).The GWR model has smooth process when constructing the farmland spatial model.The coefficients of GWR model can show the accurate influence degrees of different driving factors on the farmland at different geographical locations.The performance indices of GWR model showed that GWR model produced more accurate simulation results than other models at different times,and the improvement precision of GWR model was obvious.The global and local farmland models used in this study showed different characteristics in the spatial distributions of farmland indices at different scales,which may provide the theoretical basis for farmland protection from the influence of different driving factors.展开更多
The use of [1] Box-Cox power transformation in regression analysis is now common;in the last two decades there has been emphasis on diagnostics methods for Box-Cox power transformation, much of which has involved dele...The use of [1] Box-Cox power transformation in regression analysis is now common;in the last two decades there has been emphasis on diagnostics methods for Box-Cox power transformation, much of which has involved deletion of influential data cases. The pioneer work of [2] studied local influence on constant variance perturbation in the Box-Cox unbiased regression linear mode. Tsai and Wu [3] analyzed local influence method of [2] to assess the effect of the case-weights perturbation on the transformation-power estimator in the Box-Cox unbiased regression linear model. Many authors noted that the influential observations on the biased estimators are different from the unbiased estimators. In this paper I describe a diagnostic method for assessing the local influence on the constant variance perturbation on the transformation in the Box-Cox biased ridge regression linear model. Two real macroeconomic data sets are used to illustrate the methodologies.展开更多
Regression and autoregressive mixed models are classical models used to analyze the relationship between time series response variable and other covariates. The coefficients in traditional regression and autoregressiv...Regression and autoregressive mixed models are classical models used to analyze the relationship between time series response variable and other covariates. The coefficients in traditional regression and autoregressive mixed models are constants. However, for complicated data, the coefficients of covariates may change with time. In this article, we propose a kind of partial time-varying coefficient regression and autoregressive mixed model and obtain the local weighted least-square estimators of coefficient functions by the local polynomial technique. The asymptotic normality properties of estimators are derived under regularity conditions, and simulation studies are conducted to empirically examine the finite-sample performances of the proposed estimators. Finally, we use real data about Lake Shasta inflow to illustrate the application of the proposed model.展开更多
Regression and autoregressive mixed models are classical models used to analyze the relationship between time series response variable and other covariates. The coefficients in traditional regression and autoregressiv...Regression and autoregressive mixed models are classical models used to analyze the relationship between time series response variable and other covariates. The coefficients in traditional regression and autoregressive mixed models are constants. However, for complicated data, the coefficients of covariates may change with time. In this article, we propose a kind of partial time-varying coefficient regression and autoregressive mixed model and obtain the local weighted least-square estimators of coefficient functions by the local polynomial technique. The asymptotic normality properties of estimators are derived under regularity conditions, and simulation studies are conducted to empirically examine the finite-sample performances of the proposed estimators. Finally, we use real data about Lake Shasta inflow to illustrate the application of the proposed model.展开更多
Focusing on controlling the press-assembly quality of high-precision servo mechanism,an intelligent early warning method based on outlier data detection and linear regression is proposed.Linear regression is used to d...Focusing on controlling the press-assembly quality of high-precision servo mechanism,an intelligent early warning method based on outlier data detection and linear regression is proposed.Linear regression is used to deal with the relationship between assembly quality and press-assembly process,then the mathematical model of displacement-force in press-assembly process is established and a qualified press-assembly force range is defined for assembly quality control.To preprocess the raw dataset of displacement-force in the press-assembly process,an improved local outlier factor based on area density and P weight(LAOPW)is designed to eliminate the outliers which will result in inaccuracy of the mathematical model.A weighted distance based on information entropy is used to measure distance,and the reachable distance is replaced with P weight.Experiments show that the detection efficiency of the algorithm is improved by 5.6 ms compared with the traditional local outlier factor(LOF)algorithm,and the detection accuracy is improved by about 2%compared with the local outlier factor based on area density(LAOF)algorithm.The application of LAOPW algorithm and the linear regression model shows that it can effectively carry out intelligent early warning of press-assembly quality of high precision servo mechanism.展开更多
文摘In this study, a multivariate local quadratic polynomial regression(MLQPR) method is proposed to design a model for the sludge volume index(SVI). In MLQPR, a quadratic polynomial regression function is established to describe the relationship between SVI and the relative variables, and the important terms of the quadratic polynomial regression function are determined by the significant test of the corresponding coefficients. Moreover, a local estimation method is introduced to adjust the weights of the quadratic polynomial regression function to improve the model accuracy. Finally, the proposed method is applied to predict the SVI values in a real wastewater treatment process(WWTP). The experimental results demonstrate that the proposed MLQPR method has faster testing speed and more accurate results than some existing methods.
文摘In this article, authors introduce a method to assess local influence of obser- vations on the parameter estimates and prediction in multivariate regression model. The diagnostics under the perturbations of error variance, response variables and explanatory variables are derived, and the results are compared with those of case- deletion. Two examples are analyzed for illustration.
文摘In this paper, we try to find numerical solution of y'(x)= p(x)y(x)+g(x)+λ∫ba K(x, t)y(t)dt, y(a)=α. a≤x≤b, a≤t≤b or y'(x)= p(x)y(x)+g(x)+λ∫xa K(x, t)y(t)dt, y(a)=α. a≤x≤b, a≤t≤b by using Local polynomial regression (LPR) method. The numerical solution shows that this method is powerful in solving integro-differential equations. The method will be tested on three model problems in order to demonstrate its usefulness and accuracy.
文摘Global statistical techniques often assume homogeneity of relationships between dependent variable and predictors across space. This assumption has been criticized by statistical geographers as a fundamental weakness that may yield misleading result when it is applied to dataset with spatial context. To strengthen this weakness, a new method that accounts for heterogeneity in relationships across geographic space has been presented. This is one of the family of local spatial statistical techniques referred to as geographically weighted regression (GWR). The method captures non-stationarity of relationship in spatial data that the ordinary least square (OLS) regression fails to account for. Thus, the paper is designed to explore and analyze the spatial relationships between cholera occurrence and household sources of water supply using GIS-based GWR, also to compare the modeling fitness of OLS and GWR. Vector dataset (spatial) of the study region by state levels and statistical data (non-spatial) on cholera cases, household sources of water supply and population data were used in this exploratory analysis. The result shows that GWR is a significant improvement on the global model. Comparing both models with the AICc value and the R2 value revealed that for the former, the value is reduced from 698.7 (for OLS model) to 691.5 (for GWR model). For the latter, OLS explained 66.4 percent while GWR explained 86.7 percent. This implies that local model’s fitness is higher than global model. In addition, the empirical analysis revealed that cholera occurrence in the study region is significantly associated with household sources of water supply. This relationship, as detected by GWR, largely varies across the region.
文摘This paper proposes parametric component and nonparametric component estimators in a semiparametric regression models based on least squares and weight function's method, their strong consistency and rib mean consistency are obtained under a locally generallied Gaussinan error's structure. Finally, the author showes that the usual weight functions based on nearest neighbor method satisfy the deigned assumptions imposed.
文摘The magnetic information measured on the smartphone platform has a large fluctuation and the research of indoor localization algorithm based on smart-phone platform is less. Indoor localization algorithm on smartphone platform based on particle filter is studied. Robust local weighted regression is used to smooth the original magnetic data in the process of constructing magnetic map. Use moving average filtering model to filter the online magnetic observation data in positioning process. Compare processed online magnetic data with processed magnetic map collected by smartphone platform and the average matching error is 0.3941uT. Average positioning error is 0.229 meter when using processed online and map data.
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In this paper, auxiliary information is used to determine an estimator of finite population total using nonparametric regression under stratified random sampling. To achieve this, a model-based approach is adopted by making use of the local polynomial regression estimation to predict the nonsampled values of the survey variable y. The performance of the proposed estimator is investigated against some design-based and model-based regression estimators. The simulation experiments show that the resulting estimator exhibits good properties. Generally, good confidence intervals are seen for the nonparametric regression estimators, and use of the proposed estimator leads to relatively smaller values of RE compared to other estimators.
文摘In this paper, an overview of an important feature in statistics field has shown： the stepwise multiple linear regression. Likewise, a link between stepwise multiple linear regression and earthquakes localization has been descripted. Precisely, the aim of this research is showing how stepwise multiple linear regression contributes to solution of earthquakes localization, describing its conditions of use in HYPO71PC, a software devoted to computation of seismic sources’ collocation. This aim is reached treating a concrete case, that is computation of earthquakes localization happening on Mount Vesuvius, Italy.
文摘There are a variety of classification techniques such as neural network, decision tree, support vector machine and logistic regression. The problem of dimensionality is pertinent to many learning algorithms, and it denotes the drastic raise of computational complexity, however, we need to use dimensionality reduction methods. These methods include principal component analysis (PCA) and locality preserving projection (LPP). In many real-world classification problems, the local structure is more important than the global structure and dimensionality reduction techniques ignore the local structure and preserve the global structure. The objectives is to compare PCA and LPP in terms of accuracy, to develop appropriate representations of complex data by reducing the dimensions of the data and to explain the importance of using LPP with logistic regression. The results of this paper find that the proposed LPP approach provides a better representation and high accuracy than the PCA approach.
文摘In this paper,a class of functional-coefficient regression models is proposed and an estimation procedure based on the locally weighted least equares is suggested.This class of models,with the proposed estimation method,is a powerful means for exploratory data analysis.
文摘In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the local linear technique and the averaged method,the initial estimates of the coefficient functions are given.Second step,based on the initial estimates,the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure.The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions.Two simulated examples show that the procedure is effective.
基金The National Natural Science Foundation of China(No.61075009)the Natural Science Foundation of Jiangsu Province(No.BK2011595)the Program for New Century Excellent Talents in University of China,the Qing Lan Project of Jiangsu Province
文摘In order to improve classification accuracy, the regularized logistic regression is used to classify single-trial electroencephalogram （EEG）. A novel approach, named local sparse logistic regression （LSLR）, is proposed. The LSLR integrates the locality preserving projection regularization term into the framework of sparse logistic regression. It tries to maintain the neighborhood information of original feature space, and, meanwhile, keeps sparsity. The bound optimization algorithm and component-wise update are used to compute the weight vector in the training data, thus overcoming the disadvantage of the Newton-Raphson method and iterative re-weighted least squares （IRLS）. The classification accuracy of 80% is achieved using ten-fold cross-validation in the self-paced finger tapping data set. The results of LSLR are compared with SLR, showing the effectiveness of the proposed method.
基金Under the auspices of National Natural Science Foundation of China(No.40601073,41101192,41201571)Fundamental Research Funds for the Central Universities(No.2011PY112,2011QC041,2011QC091)Huazhong Agricultural University Scientific&Technological Self-innovation Foundation(No.2011SC21)
文摘This study used spatial autoregression(SAR)model and geographically weighted regression(GWR)model to model the spatial patterns of farmland density and its temporal change in Gucheng County,Hubei Province,China in 1999 and 2009,and discussed the difference between global and local spatial autocorrelations in terms of spatial heterogeneity and non-stationarity.Results showed that strong spatial positive correlations existed in the spatial distributions of farmland density,its temporal change and the driving factors,and the coefficients of spatial autocorrelations decreased as the spatial lag distance increased.SAR models revealed the global spatial relations between dependent and independent variables,while the GWR model showed the spatially varying fitting degree and local weighting coefficients of driving factors and farmland indices(i.e.,farmland density and temporal change).The GWR model has smooth process when constructing the farmland spatial model.The coefficients of GWR model can show the accurate influence degrees of different driving factors on the farmland at different geographical locations.The performance indices of GWR model showed that GWR model produced more accurate simulation results than other models at different times,and the improvement precision of GWR model was obvious.The global and local farmland models used in this study showed different characteristics in the spatial distributions of farmland indices at different scales,which may provide the theoretical basis for farmland protection from the influence of different driving factors.
文摘The use of [1] Box-Cox power transformation in regression analysis is now common;in the last two decades there has been emphasis on diagnostics methods for Box-Cox power transformation, much of which has involved deletion of influential data cases. The pioneer work of [2] studied local influence on constant variance perturbation in the Box-Cox unbiased regression linear mode. Tsai and Wu [3] analyzed local influence method of [2] to assess the effect of the case-weights perturbation on the transformation-power estimator in the Box-Cox unbiased regression linear model. Many authors noted that the influential observations on the biased estimators are different from the unbiased estimators. In this paper I describe a diagnostic method for assessing the local influence on the constant variance perturbation on the transformation in the Box-Cox biased ridge regression linear model. Two real macroeconomic data sets are used to illustrate the methodologies.
文摘Regression and autoregressive mixed models are classical models used to analyze the relationship between time series response variable and other covariates. The coefficients in traditional regression and autoregressive mixed models are constants. However, for complicated data, the coefficients of covariates may change with time. In this article, we propose a kind of partial time-varying coefficient regression and autoregressive mixed model and obtain the local weighted least-square estimators of coefficient functions by the local polynomial technique. The asymptotic normality properties of estimators are derived under regularity conditions, and simulation studies are conducted to empirically examine the finite-sample performances of the proposed estimators. Finally, we use real data about Lake Shasta inflow to illustrate the application of the proposed model.
文摘Regression and autoregressive mixed models are classical models used to analyze the relationship between time series response variable and other covariates. The coefficients in traditional regression and autoregressive mixed models are constants. However, for complicated data, the coefficients of covariates may change with time. In this article, we propose a kind of partial time-varying coefficient regression and autoregressive mixed model and obtain the local weighted least-square estimators of coefficient functions by the local polynomial technique. The asymptotic normality properties of estimators are derived under regularity conditions, and simulation studies are conducted to empirically examine the finite-sample performances of the proposed estimators. Finally, we use real data about Lake Shasta inflow to illustrate the application of the proposed model.
文摘Focusing on controlling the press-assembly quality of high-precision servo mechanism,an intelligent early warning method based on outlier data detection and linear regression is proposed.Linear regression is used to deal with the relationship between assembly quality and press-assembly process,then the mathematical model of displacement-force in press-assembly process is established and a qualified press-assembly force range is defined for assembly quality control.To preprocess the raw dataset of displacement-force in the press-assembly process,an improved local outlier factor based on area density and P weight(LAOPW)is designed to eliminate the outliers which will result in inaccuracy of the mathematical model.A weighted distance based on information entropy is used to measure distance,and the reachable distance is replaced with P weight.Experiments show that the detection efficiency of the algorithm is improved by 5.6 ms compared with the traditional local outlier factor(LOF)algorithm,and the detection accuracy is improved by about 2%compared with the local outlier factor based on area density(LAOF)algorithm.The application of LAOPW algorithm and the linear regression model shows that it can effectively carry out intelligent early warning of press-assembly quality of high precision servo mechanism.
