Related papers: L1-Penalized Quantile Regression in High-Dimension…
We study functional regression with random subgaussian design and real-valued response. The focus is on the problems in which the regression function can be well approximated by a functional linear model with the slope function being…
This paper considers equity premium prediction, for which mean regression can be problematic due to heteroscedasticity and heavy-tails of the error. We show advantages of quantile predictions using a novel penalized quantile regression that…
This paper studies inference in the high-dimensional linear regression model with outliers. Sparsity constraints are imposed on the vector of coefficients of the covariates. The number of outliers can grow with the sample size while their…
We consider a class of $\ell_0$-regularized linear-quadratic (LQ) optimal control problems. This class of problems is obtained by augmenting a penalizing sparsity measure to the cost objective of the standard linear-quadratic regulator…
Quantile regression (QR) is becoming increasingly popular due to its relevance in many scientific investigations. There is a great amount of work about linear and nonlinear QR models. Specifically, nonparametric estimation of the…
We investigate conditions for the unique recoverability of sparse integer-valued signals from a small number of linear measurements. Both the objective of minimizing the number of nonzero components, the so-called $\ell_0$-norm, as well as…
Sparse clustering, which aims to find a proper partition of an extremely high-dimensional data set with redundant noise features, has been attracted more and more interests in recent years. The existing studies commonly solve the problem in…
This paper studies large $N$ and large $T$ conditional quantile panel data models with interactive fixed effects. We propose a nuclear norm penalized estimator of the coefficients on the covariates and the low-rank matrix formed by the…
We consider quantile regression processes from censored data under dependent data structures and derive a uniform Bahadur representation for those processes. We also consider cases where the dimension of the parameter in the quantile…
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…
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…
This paper considers sparsity in linear regression under the restriction that the regression weights sum to one. We propose an approach that combines $\ell_0$- and $\ell_1$-regularization. We compute its solution by adapting a recent…
We propose a generalization of the linear panel quantile regression model to accommodate both \textit{sparse} and \textit{dense} parts: sparse means while the number of covariates available is large, potentially only a much smaller number…
Popular iterative algorithms such as boosting methods and coordinate descent on linear models converge to the maximum $\ell_1$-margin classifier, a.k.a. sparse hard-margin SVM, in high dimensional regimes where the data is linearly…
Quantile regression is a very important tool to explore the relationship between the response variable and its covariates. Motivated by mean regression with LASSO for compositional covariates proposed by Lin et al. (2014), we consider…
Quantile regression (QR) is a principal regression method for analyzing the impact of covariates on outcomes. The impact is described by the conditional quantile function and its functionals. In this paper we develop the nonparametric…
This paper develops a semi-parametric procedure for estimation of unconditional quantile partial effects using quantile regression coefficients. The estimator is based on an identification result showing that, for continuous covariates,…
P-splines are penalized B-splines, in which finite order differences in coefficients are typically penalized with an $\ell_2$ norm. P-splines can be used for semiparametric regression and can include random effects to account for…
We proposed a new penalized method in this paper to solve sparse Poisson Regression problems. Being different from $\ell_1$ penalized log-likelihood estimation, our new method can be viewed as penalized weighted score function method. We…
Quantile regression is a powerful tool capable of offering a richer view of the data as compared to least-squares regression. Quantile regression is typically performed individually on a few quantiles or a grid of quantiles without…