Efficient Shrinkage Estimation about the Partially Linear Varying Coefficient Model with Random Effect for Longitudinal Data

In this paper, an efficient shrinkage estimation procedure for the partially linear varying coefficient model (PLVC) with random effect is considered. By selecting the significant variable and estimating the nonzero coefficient, the model structure specification is accomplished by introducing a novel penalized estimating equation. Under some mild conditions, the asymptotic properties for the proposed model selection and estimation results, such as the sparsity and oracle property, are established. Some numerical simulation studies and a real data analysis are presented to examine the finite sample performance of the procedure.

Regularized Inverse Covariance Estimation for Longitudinal Data with Informative Dropout

This paper proposes a novel method for estimating the sparse inverse covariance matrixfor longitudinal data with informative dropouts. Based on the modified Cholesky decomposition,the sparse inverse covariance matrix is modelled by the autoregressive regression model,which guarantees the positive definiteness of the covariance matrix. To account for the informativedropouts, we then propose a penalized estimating equation method using the inverse probabilityweighting approach. The informative dropout propensity parameters are estimated by the generalizedmethod of moments. The asymptotic properties are investigated for the resulting estimators.Finally, we illustrate the effectiveness and feasibility of the proposed method through Monte Carlosimulations and a practical application.

Double Penalized Variable Selection Procedure for Partially Linear Models with Longitudinal Data

Based on the double penalized estimation method,a new variable selection procedure is proposed for partially linear models with longitudinal data.The proposed procedure can avoid the effects of the nonparametric estimator on the variable selection for the parameters components.Under some regularity conditions,the rate of convergence and asymptotic normality of the resulting estimators are established.In addition,to improve efficiency for regression coefficients,the estimation of the working covariance matrix is involved in the proposed iterative algorithm.Some simulation studies are carried out to demonstrate that the proposed method performs well.

Degrees of freedom in low rank matrix estimation

The objective of this paper is to quantify the complexity of rank and nuclear norm constrained methods for low rank matrix estimation problems. Specifically, we derive analytic forms of the degrees of freedom for these types of estimators in several common settings. These results provide efficient ways of comparing different estimators and eliciting tuning parameters. Moreover, our analyses reveal new insights on the behavior of these low rank matrix estimators. These observations are of great theoretical and practical importance. In particular, they suggest that, contrary to conventional wisdom, for rank constrained estimators the total number of free parameters underestimates the degrees of freedom, whereas for nuclear norm penalization, it overestimates the degrees of freedom. In addition, when using most model selection criteria to choose the tuning parameter for nuclear norm penalization, it oftentimes suffices to entertain a finite number of candidates as opposed to a continuum of choices. Numerical examples are also presented to illustrate the practical implications of our results.

Variable Selection in Joint Location, Scale and Skewness Models of the Skew-Normal Distribution

Variable selection is an important research topic in modern statistics, traditional variable selection methods can only select the mean model and(or) the variance model, and cannot be used to select the joint mean, variance and skewness models. In this paper, the authors propose the joint location, scale and skewness models when the data set under consideration involves asymmetric outcomes,and consider the problem of variable selection for our proposed models. Based on an efficient unified penalized likelihood method, the consistency and the oracle property of the penalized estimators are established. The authors develop the variable selection procedure for the proposed joint models, which can efficiently simultaneously estimate and select important variables in location model, scale model and skewness model. Simulation studies and body mass index data analysis are presented to illustrate the proposed methods.

Local Influence Analysis for Semiparametric Reproductive Dispersion Nonlinear Models

The present paper proposes a semiparametric reproductive dispersion nonlinear model （SRDNM） which is an extension of the nonlinear reproductive dispersion models and the semiparameter regression models. Maximum penalized likelihood estimates （MPLEs） of unknown parameters and nonparametric functions in SRDNM are presented. Assessment of local influence for various perturbation schemes are investigated. Some local influence diagnostics are given. A simulation study and a real example are used to illustrate the proposed methodologies.