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A novel approach to quantile estimation in multivariate linear regression models with change-points is proposed: the change-point detection and the model estimation are both performed automatically, by adopting either the quantile fused…
This paper develops a new framework, called modular regression, to utilize auxiliary information -- such as variables other than the original features or additional data sets -- in the training process of linear models. At a high level, our…
We propose a generalized functional linear regression model for a regression situation where the response variable is a scalar and the predictor is a random function. A linear predictor is obtained by forming the scalar product of the…
We propose a novel method to model nonlinear regression problems by adapting the principle of penalization to Partial Least Squares (PLS). Starting with a generalized additive model, we expand the additive component of each variable in…
Data-driven methods for modeling dynamic systems have received considerable attention as they provide a mechanism for control synthesis directly from the observed time-series data. In the absence of prior assumptions on how the time-series…
When we are interested in high-dimensional system and focus on classification performance, the $\ell_{1}$-penalized logistic regression is becoming important and popular. However, the Lasso estimates could be problematic when penalties of…
Robust estimators for generalized linear models (GLMs) are not easy to develop due to the nature of the distributions involved. Recently, there has been growing interest in robust estimation methods, particularly in contexts involving a…
We study the Cox models with semiparametric relative risk, which can be partially linear with one nonparametric component, or multiple additive or nonadditive nonparametric components. A penalized partial likelihood procedure is proposed to…
We propose generalized additive partial linear models for complex data which allow one to capture nonlinear patterns of some covariates, in the presence of linear components. The proposed method improves estimation efficiency and increases…
In this paper, we are concerned with how to select significant variables in semiparametric modeling. Variable selection for semiparametric regression models consists of two components: model selection for nonparametric components and…
In this paper, we study the nonparametric linear model, when the error process is a dependent Gaussian process. We focus on the estimation of the mean vector via a model selection approach. We first give the general theoretical form of the…
We consider the linear regression problem under semi-supervised settings wherein the available data typically consists of: (i) a small or moderate sized 'labeled' data, and (ii) a much larger sized 'unlabeled' data. Such data arises…
One fundamental statistical question for research areas such as precision medicine and health disparity is about discovering effect modification of treatment or exposure by observed covariates. We propose a semiparametric framework for…
This study examines the optimal selections of bandwidth and semi-metric for a functional partial linear model. Our proposed method begins by estimating the unknown error density using a kernel density estimator of residuals, where the…
We propose a new prediction method for multivariate linear regression problems where the number of features is less than the sample size but the number of outcomes is extremely large. Many popular procedures, such as penalized regression…
Because of the advance in technologies, modern statistical studies often encounter linear models with the number of explanatory variables much larger than the sample size. Estimation and variable selection in these high-dimensional problems…
The penalized profile sampler for semiparametric inference is an extension of the profile sampler method (Lee, Kosorok and Fine, 2005) obtained by profiling a penalized log-likelihood. The idea is to base inference on the posterior…
We mainly study the M-estimation method for the high-dimensional linear regression model, and discuss the properties of M-estimator when the penalty term is the local linear approximation. In fact, M-estimation method is a framework, which…
This paper considers the problem of semi-parametric proportional hazards model fitting for interval, left and right censored survival times. We adopt a more versatile penalized likelihood method to estimate the baseline hazard and the…
This paper analyzes the classical linear regression model with measurement errors in all the variables. First, we provide necessary and sufficient conditions for identification of the coefficients. We show that the coefficients are not…