Restricted Statistical Inference And Variable Selection Via Adaptive LASSO For Partially Linear Errors-in-function Models

As an important class of semi-parametric models in mathematics and statistics,partially linear model has been conducted by many scholars. Now partially linear model has been widely used in modern statistics for it can retain the flexibility of nonparametric models and ease of interpretation of linear regression models. However,the real problem is often more complex and difficult to handle. For example, the measurement error exists commonly and can not be ignored. So the study of partially linear model with measurement errors is of more practical value.Considering partially linear errors-in-function model, restricted statistical inference for the parametric component and variable selection problem are studied in this paper.For the parametric component’s statistical inference, a restricted estimator for the parameter is derived and is demonstrated to be asymptotic normal. Then, a test procedure based on the generalized likelihood ratio statistic is proposed. It is proven that the Wilks phenomenon for errors in function still holds under some mild conditions.Finally, a simulation study is carried out to examine the finite sample performance of the proposed estimators and the validity of the test statistic.Variables selection is also crucial as an important part of model setting. For the LASSO is a popular technique for simultaneous estimation and variable selection,Adaptive LASSO is a new version of the lasso whose weights are used for penalizing different coefficients in the1 L penalty and have been proven that Adaptive LASSO enjoys the oracle properties. This paper show that Adaptive LASSO also can be applied to partially linear errors-in-function models. Firstly, Adaptive LASSO estimators are obtained via weighting an Adaptive LASSO penalties on profile least squares estimates.Then under some regular conditions, the estimator’s consistency and asymptotic normality are investigated, and it is proved that the adaptive LASSO estimator enjoys the oracle properties. Finally, Monte Carlo simulation study is carried out to evaluate the performance of the proposed variable selection procedure in finite sample, results indicating that the adaptive LASSO estimator behaves well comparing with LASSO SCAD MCP.