In this paper, we consider the problem of simultaneous variable selection and estimation for varying-coefficient partially linear models in a “small <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$n$$</EquationSource> </InlineEquation>, large <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$p$$</EquationSource> </InlineEquation>” setting, when the number of coefficients in the linear part diverges with sample size while the number of varying...</equationsource></inlineequation></equationsource></inlineequation>

This article develops a mean field variational Bayes approximation algorithm for posterior inferences of the recently proposed partially linear additive models with simultaneous and automatic variable selection and linear/nonlinear component identification abilities. To solve the problem induced...

Separation of the linear and nonlinear components in additive models based on penalized likelihood has received attention recently. However, it remains unknown whether consistent separation is possible in generalized additive models, and how high dimensionality is allowed. In this article, we...

In this paper, we consider the partially linear single-index models with longitudinal data. We propose the bias-corrected quadratic inference function (QIF) method to estimate the parameters in the model by accounting for the within-subject correlation. Asymptotic properties for the proposed...

We consider penalized singular value decomposition (SVD) for a (noisy) data matrix when the left singular vector has a sparse structure and the right singular vector is a discretized function. Such situations typically arise from spatio-temporal data where only some small spatial regions are...

For linear models with a diverging number of parameters, it has recently been shown that modified versions of Bayesian information criterion (BIC) can identify the true model consistently. However, in many cases there is little justification that the effects of the covariates are actually...

We consider the problem of variable selection for the generalized linear models (GLMs) with longitudinal data. An automatic variable selection procedure is developed using smooth-threshold generalized estimating equations (SGEE). The proposed procedure automatically eliminates inactive...