In this short note, we demonstrate that Schwarz’s criterion, which has been used frequently in the literature on quantile regression, is consistent in variable selection. In particular, due to the recent interest in penalized likelihood for variable selection, we also show that Schwarz’s...

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...

In this paper, following the results presented in Liu's work [Liu, A.Y., 2002. Efficient estimation of two seemingly unrelated regression equations. Journal of Multivariate Analysis 82, 445-456], we first represent the Gauss-Markov estimator of the regression parameter as a matrix series, and...

type="main" xml:id="rssb12066-abs-0001" <title type="main">Summary</title> <p>We consider heteroscedastic regression models where the mean function is a partially linear single-index model and the variance function depends on a generalized partially linear single-index model. We do not insist that the variance function...</p>

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...

We propose the penalized estimator with the smoothly clipped absolute deviation (SCAD) penalty for varying coefficient time series models, which in autoregressive models actually performs lag order selection. Theoretical properties are established. Some numerical examples are also presented.

We study in this paper the consistency of Bayesian estimation of a piecewise constant function defined on [0,1] with observations on a grid, using the method in Barron et al. [1999. The consistency of posterior distributions in nonparametric problems. Ann. Statist. 27, 536-561.] In particular,...

We consider the augmented Lagrangian method (ALM) as a solver for the fused lasso signal approximator (FLSA) problem. The ALM is a dual method in which squares of the constraint functions are added as penalties to the Lagrangian. In order to apply this method to FLSA, two types of auxiliary...

Generalized varying coefficient partially linear models are a flexible class of semiparametric models that deal with data with different types of responses. In this paper, we focus on polynomial spline estimator as a computationally easier alternative to the more commonly used local polynomial...