The varying-coefficient model is flexible and powerful for modeling the dynamic changes of regression coefficients. We study the problem of variable selection and estimation in this model in the sparse, high- dimensional case. We develop a concave group selection approach for this problem using basis function expansion and study its theoretical and empirical properties. We also apply the group Lasso for variable selection and estimation in this model and study its properties. Under appropriate conditions, we show that the group least absolute shrinkage and selection operator （Lasso） selects a model whose dimension is comparable to the underlying mode], regardless of the large number of unimportant variables. In order to improve the selection results, we show that the group minimax concave penalty （MCP） has the oracle selection property in the sense that it correctly selects important variables with probability converging to one under suitable conditions. By comparison, the group Lasso does not have the oracle selection property. In the simulation parts, we apply the group Lasso and the group MCP. At the same time, the two approaches are evaluated using simulation and demonstrated on a data example.
This paper studies estimation of a partially specified spatial autoregressive model with heteroskedas- ticity error term. Under the assumption of exogenous regressors and exogenous spatial weighting matrix, the unknown parameter is estimated by applying the instrumental variable estimation. Under certain sufficient conditions, the proposed estimator for the finite dimensional parameters is shown to be root-n consistent and asymptotically normally distributed; The proposed estimator for the unknown function is shown to be consis- tent and asymptotically distributed as well, though at a rate slower than root-n. Consistent estimators for the asymptotic variance-covariance matrices of both estimators are provided. Monte Carlo simulations suggest that the proposed procedure has some practical value.
Missing data mechanism often depends on the values of the responses,which leads to nonignorable nonresponses.In such a situation,inference based on approaches that ignore the missing data mechanism could not be valid.A crucial step is to model the nature of missingness.We specify a parametric model for missingness mechanism,and then propose a conditional score function approach for estimation.This approach imputes the score function by taking the conditional expectation of the score function for the missing data given the available information.Inference procedure is then followed by replacing unknown terms with the related nonparametric estimators based on the observed data.The proposed score function does not suffer from the non-identifiability problem,and the proposed estimator is shown to be consistent and asymptotically normal.We also construct a confidence region for the parameter of interest using empirical likelihood method.Simulation studies demonstrate that the proposed inference procedure performs well in many settings.We apply the proposed method to a data set from research in a growth hormone and exercise intervention study.
