In this article, we focus on the semi-parametric error-in-variables model with missing responses: , where yi are the response variables missing at random, are design points, ζi are the potential variables observed wi...In this article, we focus on the semi-parametric error-in-variables model with missing responses: , where yi are the response variables missing at random, are design points, ζi are the potential variables observed with measurement errors μi, the unknown slope parameter ß?and nonparametric component g(·) need to be estimated. Here we choose two different approaches to estimate ß?and g(·). Under appropriate conditions, we study the strong consistency for the proposed estimators.展开更多
This paper simultaneously investigates variable selection and imputation estimation of semiparametric partially linear varying-coefficient model in that case where there exist missing responses for cluster data. As is...This paper simultaneously investigates variable selection and imputation estimation of semiparametric partially linear varying-coefficient model in that case where there exist missing responses for cluster data. As is well known, commonly used approach to deal with missing data is complete-case data. Combined the idea of complete-case data with a discussion of shrinkage estimation is made on different cluster. In order to avoid the biased results as well as improve the estimation efficiency, this article introduces Group Least Absolute Shrinkage and Selection Operator (Group Lasso) to semiparametric model. That is to say, the method combines the approach of local polynomial smoothing and the Least Absolute Shrinkage and Selection Operator. In that case, it can conduct nonparametric estimation and variable selection in a computationally efficient manner. According to the same criterion, the parametric estimators are also obtained. Additionally, for each cluster, the nonparametric and parametric estimators are derived, and then compute the weighted average per cluster as finally estimators. Moreover, the large sample properties of estimators are also derived respectively.展开更多
文摘In this article, we focus on the semi-parametric error-in-variables model with missing responses: , where yi are the response variables missing at random, are design points, ζi are the potential variables observed with measurement errors μi, the unknown slope parameter ß?and nonparametric component g(·) need to be estimated. Here we choose two different approaches to estimate ß?and g(·). Under appropriate conditions, we study the strong consistency for the proposed estimators.
文摘This paper simultaneously investigates variable selection and imputation estimation of semiparametric partially linear varying-coefficient model in that case where there exist missing responses for cluster data. As is well known, commonly used approach to deal with missing data is complete-case data. Combined the idea of complete-case data with a discussion of shrinkage estimation is made on different cluster. In order to avoid the biased results as well as improve the estimation efficiency, this article introduces Group Least Absolute Shrinkage and Selection Operator (Group Lasso) to semiparametric model. That is to say, the method combines the approach of local polynomial smoothing and the Least Absolute Shrinkage and Selection Operator. In that case, it can conduct nonparametric estimation and variable selection in a computationally efficient manner. According to the same criterion, the parametric estimators are also obtained. Additionally, for each cluster, the nonparametric and parametric estimators are derived, and then compute the weighted average per cluster as finally estimators. Moreover, the large sample properties of estimators are also derived respectively.
