Related papers: Penalized Estimation in Additive Regression with H…
We suggest a new method, called Functional Additive Regression, or FAR, for efficiently performing high-dimensional functional regression. FAR extends the usual linear regression model involving a functional predictor, $X(t)$, and a scalar…
The ultimate goal of regression analysis is to obtain information about the conditional distribution of a response given a set of explanatory variables. This goal is, however, seldom achieved because most established regression models only…
Classical penalized likelihood regression problems deal with the case that the independent variables data are known exactly. In practice, however, it is common to observe data with incomplete covariate information. We are concerned with a…
Penalties that induce smoothness are common in nonparametric regression. In many settings, the amount of smoothness in the data generating function will not be known. Simon and Shojaie (2021) derived convergence rates for nonparametric…
Asymmetry along with heteroscedasticity or contamination often occurs with the growth of data dimensionality. In ultra-high dimensional data analysis, such irregular settings are usually overlooked for both theoretical and computational…
Sparse covariates are frequent in classification and regression problems and in these settings the task of variable selection is usually of interest. As it is well known, sparse statistical models correspond to situations where there are…
We develop a continuous-time penalized regression framework for the estimation of time-varying coefficients and variable selection when both the response and covariates are It\^o semimartingales with jumps. The coefficient paths are…
This paper gives a comprehensive treatment of the convergence rates of penalized spline estimators for simultaneously estimating several leading principal component functions, when the functional data is sparsely observed. The penalized…
Penalized regression has become a standard tool for model building across a wide range of application domains. Common practice is to tune the amount of penalization to tradeoff bias and variance or to optimize some other measure of…
Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel…
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…
We study a functional linear regression model that deals with functional responses and allows for both functional covariates and high-dimensional vector covariates. The proposed model is flexible and nests several functional regression…
This paper focuses on a semiparametric regression model in which the response variable is explained by the sum of two components. One of them is parametric (linear), the corresponding explanatory variable is measured with additive error and…
In supervised learning, we typically leverage a fully labeled dataset to design methods for function estimation or prediction. In many practical situations, we are able to obtain alternative feedback, possibly at a low cost. A broad goal is…
In genetic studies, not only can the number of predictors obtained from microarray measurements be extremely large, there can also be multiple response variables. Motivated by such a situation, we consider semiparametric dimension reduction…
For data with high-dimensional covariates but small to moderate sample sizes, the analysis of single datasets often generates unsatisfactory results. The integrative analysis of multiple independent datasets provides an effective way of…
For multivariate nonparametric regression, functional analysis-of-variance (ANOVA) modeling aims to capture the relationship between a response and covariates by decomposing the unknown function into various components, representing main…
Motivated by value function estimation in reinforcement learning, we study statistical linear inverse problems, i.e., problems where the coefficients of a linear system to be solved are observed in noise. We consider penalized estimators,…
In this article, we propose a penalized high dimensional semiparametric model average quantile prediction approach that is robust for forecasting the conditional quantile of the response. We consider a two-step estimation procedure. In the…
Sparse additive modeling is a class of effective methods for performing high-dimensional nonparametric regression. In this work we show how shape constraints such as convexity/concavity and their extensions, can be integrated into additive…