Related papers: SCAD-penalized regression in high-dimensional part…

Traditionally, spline or kernel approaches in combination with parametric estimation are used to infer the linear coefficient (fixed effects) in a partially linear mixed-effects model for repeated measurements. Using machine learning…

We consider high-dimensional binary classification by sparse logistic regression. We propose a model/feature selection procedure based on penalized maximum likelihood with a complexity penalty on the model size and derive the non-asymptotic…

In high-dimensional model selection problems, penalized simple least-square approaches have been extensively used. This paper addresses the question of both robustness and efficiency of penalized model selection methods, and proposes a…

We consider both $\ell _{0}$-penalized and $\ell _{0}$-constrained quantile regression estimators. For the $\ell _{0}$-penalized estimator, we derive an exponential inequality on the tail probability of excess quantile prediction risk and…

An adaptive nonparametric estimation procedure is constructed for heteroscedastic regression when the noise variance depends on the unknown regression. A non-asymptotic upper bound for a quadratic risk (oracle inequality) is obtained

This work studies the multi-task functional linear regression models where both the covariates and the unknown regression coefficients (called slope functions) are curves. For slope function estimation, we employ penalized splines to…

We build penalized least-squares estimators using the slope heuristic and resampling penalties. We prove oracle inequalities for the selected estimator with leading constant asymptotically equal to 1. We compare the practical performances…

This paper considers the quantile regression approach for partially linear spatial autoregressive models with possibly varying coefficients. B-spline is employed for the approximation of varying coefficients. The instrumental variable…

Estimating network formation models with degree heterogeneity raises two problems in empirical networks. First, agents that send no links, receive no links, or link to all remaining agents can make the fixed-effects MLE fail to exist.…

We study a regression problem where for some part of the data we observe both the label variable ($Y$) and the predictors (${\bf X}$), while for other part of the data only the predictors are given. Such a problem arises, for example, when…

We study the distributions of the LASSO, SCAD, and thresholding estimators, in finite samples and in the large-sample limit. The asymptotic distributions are derived for both the case where the estimators are tuned to perform consistent…

Assume one observes independent categorical variables or, equivalently, one observes the corresponding multinomial variables. Estimating the distribution of the observed sequence amounts to estimating the expectation of the multinomial…

We consider the estimation of a regression function with random design and heteroscedastic noise in a nonparametric setting. More precisely, we address the problem of characterizing the optimal penalty when the regression function is…

In the context of a linear model with a sparse coefficient vector, exponential weights methods have been shown to be achieve oracle inequalities for prediction. We show that such methods also succeed at variable selection and estimation…

We propose a new method for the simultaneous selection and estimation of multivariate sparse additive models with correlated errors. Our method called Covariance Assisted Multivariate Penalized Additive Regression (CoMPAdRe) simultaneously…

Model selection and sparse recovery are two important problems for which many regularization methods have been proposed. We study the properties of regularization methods in both problems under the unified framework of regularized least…

Maximum likelihood estimation of large Markov-switching vector autoregressions (MS-VARs) can be challenging or infeasible due to parameter proliferation. To accommodate situations where dimensionality may be of comparable order to or…

This paper studies the problem of estimating a large coefficient matrix in a multiple response linear regression model when the coefficient matrix could be both of low rank and sparse in the sense that most nonzero entries concentrate on a…

A new partial functional linear regression model for panel data with time varying parameters is introduced. The parameter vector of the multivariate model component is allowed to be completely time varying while the function-valued…

We consider parameter inference for linear quantile regression with non-stationary predictors and errors, where the regression parameters are subject to inequality constraints. We show that the constrained quantile coefficient estimators…