In this article, a novel adaptive estimation is proposed for varying coefficient models. Unlike the traditional least squares based methods, the proposed approach can adapt to different error distributions. An efficient EM algorithm is provided to implement the proposed estimation. The...

Given any countable collection of regression procedures (e.g., kernel, spline, wavelet, local polynomial, neural nets, etc.), we show that a single adaptive procedure can be constructed to share their advantages to a great extent in terms of global squared L2 risk. The combined procedure...

In this paper, we focus on the variable selection for semiparametric varying coefficient partially linear models with longitudinal data. A new variable selection procedure is proposed based on the combination of the basis function approximations and quadratic inference functions. The proposed...

We study a new approach to simultaneous variable selection and estimation via random-effect models. Introducing random effects as the solution of a regularization problem is a flexible paradigm and accommodates likelihood interpretation for variable selection. This approach leads to a new type...

In this paper, the high-dimensional sparse linear regression model is considered, where the overall number of variables is larger than the number of observations. We investigate the L1 penalized least absolute deviation method. Different from most of the other methods, the L1 penalized LAD...

In this paper we are concerned with detecting the true structure of a varying-coefficient partially linear model. The first issue is to identify whether a coefficient is parametric. The second issue is to select significant covariates in both nonparametric and parametric portions. In order to...

Chen et al. (2010) [1] propose a unified method–coordinate-independent sparse estimation (CISE)–that is able to simultaneously achieve sparse sufficient dimension reduction and screen out irrelevant and redundant variables efficiently. However, its attractive features depend on the...

We propose a criterion for variable selection in discriminant analysis. This criterion permits to arrange the variables in decreasing order of adequacy for discrimination, so that the variable selection problem reduces to that of the estimation of suitable permutation and dimensionality. Then,...

It is rather challenging for current variable selectors to handle situations where the number of covariates under consideration is ultra-high. Consider a motivating clinical trial of the drug bortezomib for the treatment of multiple myeloma, where overall survival and expression levels of 44760...

In this article, we consider variable selection in robust regression models for longitudinal data. We propose a penalized robust estimating equation to estimate the regression parameters and to select the important covariate variables simultaneously. Under some regularity conditions, we show the...