Related papers: Retire: Robust Expectile Regression in High Dimens…
The curse of dimensionality is a recognized challenge in nonparametric estimation. This paper develops a new L0-norm regularization approach to the convex quantile and expectile regressions for subset variable selection. We show how to use…
Statistical methods with empirical likelihood (EL) are appealing and effective especially in conjunction with estimating equations through which useful data information can be adaptively and flexibly incorporated. It is also known in the…
Quadratic regression goes beyond the linear model by simultaneously including main effects and interactions between the covariates. The problem of interaction estimation in high dimensional quadratic regression has received extensive…
We propose a penalized orthogonal-components regression (POCRE) for large p small n data. Orthogonal components are sequentially constructed to maximize, upon standardization, their correlation to the response residuals. A new penalization…
Regularization methods allow one to handle a variety of inferential problems where there are more covariates than cases. This allows one to consider a potentially enormous number of covariates for a problem. We exploit the power of these…
The response envelope model provides substantial efficiency gains over the standard multivariate linear regression by identifying the material part of the response to the model and by excluding the immaterial part. In this paper, we propose…
We investigate the optimality for model selection of the so-called slope heuristics, $V$-fold cross-validation and $V$-fold penalization in a heteroscedastic with random design regression context. We consider a new class of linear models…
This paper carries out a large dimensional analysis of a variation of kernel ridge regression that we call \emph{centered kernel ridge regression} (CKRR), also known in the literature as kernel ridge regression with offset. This modified…
The fixed-effects model estimates the regressor effects on the mean of the response, which is inadequate to summarize the variable relationships in the presence of heteroscedasticity. In this paper, we adapt the asymmetric least squares…
Robust methods, though ubiquitous in practice, are yet to be fully understood in the context of regularized estimation and high dimensions. Even simple questions become challenging very quickly. For example, classical statistical theory…
Considering censored outcomes in survival analysis can lead to quite complex results in the model setting of causal inference. Causal inference has attracted a lot of attention over the past few years, but little research has been done on…
High-dimensional penalized rank regression is a powerful tool for modeling high-dimensional data due to its robustness and estimation efficiency. However, the non-smoothness of the rank loss brings great challenges to the computation. To…
Kernel ridge regression (KRR) is a widely used nonparametric method due to its strong theoretical guarantees and computational convenience. However, standard KRR does not distinguish between linear and nonlinear components in the signal,…
In many practical applications, regression models are employed to uncover relationships between predictors and a response variable, yet the common assumption of constant error variance is frequently violated. This issue is further…
Models defined by moment conditions are at the center of structural econometric estimation, but economic theory is mostly agnostic about moment selection. While a large pool of valid moments can potentially improve estimation efficiency, in…
We study a sparse negative binomial regression (NBR) for count data by showing the non-asymptotic advantages of using the elastic-net estimator. Two types of oracle inequalities are derived for the NBR's elastic-net estimates by using the…
This paper studies simultaneous feature selection and extraction in supervised and unsupervised learning. We propose and investigate selective reduced rank regression for constructing optimal explanatory factors from a parsimonious subset…
We consider high-dimensional generalized linear models with Lipschitz loss functions, and prove a nonasymptotic oracle inequality for the empirical risk minimizer with Lasso penalty. The penalty is based on the coefficients in the linear…
We propose a new sparsity-smoothness penalty for high-dimensional generalized additive models. The combination of sparsity and smoothness is crucial for mathematical theory as well as performance for finite-sample data. We present a…
In this study, we propose shrinkage methods based on {\it generalized ridge regression} (GRR) estimation which is suitable for both multicollinearity and high dimensional problems with small number of samples (large $p$, small $n$). Also,…