Related papers: Adaptive Estimation In High-Dimensional Additive M…
This article describes a full Bayesian treatment for simultaneous fixed-effect selection and parameter estimation in high-dimensional generalized linear mixed models. The approach consists of using a Bayesian adaptive Lasso penalty for…
It is known that the Thresholded Lasso (TL), SCAD or MCP correct intrinsic estimation bias of the Lasso. In this paper we propose an alternative method of improving the Lasso for predictive models with general convex loss functions which…
The Highly Adaptive Lasso (HAL) delivers unprecedented guarantees in nonparametric minimum loss estimation under minimal smoothness assumptions, such as dimension-free minimax optimal rates. However, the practical use of HAL has been…
Penalized regression is an attractive framework for variable selection problems. Often, variables possess a grouping structure, and the relevant selection problem is that of selecting groups, not individual variables. The group lasso has…
Nowadays an increasing amount of data is available and we have to deal with models in high dimension (number of covariates much larger than the sample size). Under sparsity assumption it is reasonable to hope that we can make a good…
We consider the problem of fitting the parameters of a high-dimensional linear regression model. In the regime where the number of parameters $p$ is comparable to or exceeds the sample size $n$, a successful approach uses an…
We consider the problem of simultaneous variable selection and constant coefficient identification in high-dimensional varying coefficient models based on B-spline basis expansion. Both objectives can be considered as some type of model…
Nowadays, several data analysis problems require for complexity reduction, mainly meaning that they target at removing the non-influential covariates from the model and at delivering a sparse model. When categorical covariates are present,…
Demanding sparsity in estimated models has become a routine practice in statistics. In many situations, we wish to require that the sparsity patterns attained honor certain problem-specific constraints. Hierarchical sparse modeling (HSM)…
This paper proposes a multi-stage projection-based Lasso procedure for the semiparametric sample selection model in high-dimensional settings under a weak nonparametric restriction on the selection correction. In particular, the number of…
We study theoretical properties of regularized robust M-estimators, applicable when data are drawn from a sparse high-dimensional linear model and contaminated by heavy-tailed distributions and/or outliers in the additive errors and…
Sparse penalized quantile regression provides an effective framework for variable selection and robust estimation in high-dimensional data analysis. When ex planatory variables are organized into groups, achieving sparsity both within and…
The $\ell_1$-penalized method, or the Lasso, has emerged as an important tool for the analysis of large data sets. Many important results have been obtained for the Lasso in linear regression which have led to a deeper understanding of…
High-dimensional statistical inference deals with models in which the the number of parameters p is comparable to or larger than the sample size n. Since it is usually impossible to obtain consistent procedures unless $p/n\rightarrow0$, a…
Data subject to heavy-tailed errors are commonly encountered in various scientific fields, especially in the modern era with explosion of massive data. To address this problem, procedures based on quantile regression and Least Absolute…
The Lasso is an attractive technique for regularization and variable selection for high-dimensional data, where the number of predictor variables $p_n$ is potentially much larger than the number of samples $n$. However, it was recently…
Consider the problem of minimizing the expected value of a (possibly nonconvex) cost function parameterized by a random (vector) variable, when the expectation cannot be computed accurately (e.g., because the statistics of the random…
We look into the nonparametric regression estimation with additive and multiplicative noise and construct adaptive thresholding estimators based on Laguerre series. The proposed approach achieves asymptotically near-optimal convergence…
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…
There are proposals that extend the classical generalized additive models (GAMs) to accommodate high-dimensional data ($p>>n$) using group sparse regularization. However, the sparse regularization may induce excess shrinkage when estimating…