Related papers: High Dimensional Analysis of Variance in Multivari…
Empirically, large-scale deep learning models often satisfy a neural scaling law: the test error of the trained model improves polynomially as the model size and data size grow. However, conventional wisdom suggests the test error consists…
We investigate the problem of statistical inference for logistic regression with high-dimensional covariates in settings where dependence among individuals is induced by an underlying Markov random field. Going beyond the pairwise…
We propose a likelihood ratio based inferential framework for high dimensional semiparametric generalized linear models. This framework addresses a variety of challenging problems in high dimensional data analysis, including incomplete…
Variable selection plays a fundamental role in high-dimensional data analysis. Various methods have been developed for variable selection in recent years. Well-known examples are forward stepwise regression (FSR) and least angle regression…
In this paper, we develop invariance-based procedures for testing and inference in high-dimensional regression models. These procedures, also known as randomization tests, provide several important advantages. First, for the global null…
Standard approaches for variable selection in linear models are not tailored to deal properly with high-dimensional and incomplete data. Currently, methods dedicated to high-dimensional data handle missing values by ad-hoc strategies, like…
Statistical analysis of high-dimensional functional times series arises in various applications. Under this scenario, in addition to the intrinsic infinite-dimensionality of functional data, the number of functional variables can grow with…
We propose a new measure of variable importance in high-dimensional regression based on the change in the LASSO solution path when one covariate is left out. The proposed procedure provides a novel way to calculate variable importance and…
We propose a general method for constructing confidence intervals and statistical tests for single or low-dimensional components of a large parameter vector in a high-dimensional model. It can be easily adjusted for multiplicity taking…
We propose a data segmentation methodology for the high-dimensional linear regression problem where regression parameters are allowed to undergo multiple changes. The proposed methodology, MOSEG, proceeds in two stages: first, the data are…
We propose a new lack-of-fit test for quantile regression models that is suitable even with high-dimensional covariates. The test is based on the cumulative sum of residuals with respect to unidimensional linear projections of the…
Multivariate linear regressions are widely used statistical tools in many applications to model the associations between multiple related responses and a set of predictors. To infer such associations, it is often of interest to test the…
Linear regression is a fundamental and popular statistical method. There are various kinds of linear regression, such as mean regression and quantile regression. In this paper, we propose a new one called distribution regression, which…
This article is concerned with simultaneous tests on linear regression coefficients in high-dimensional settings. When the dimensionality is larger than the sample size, the classic $F$-test is not applicable since the sample covariance…
A new, coordinate-free (geometric) approach to multivariate statistical analysis. General multivariate linear models and linear hypotheses are defined in geometric form. A method of constructing statistical criteria is defined for linear…
Distributional approximations of (bi--) linear functions of sample variance-covariance matrices play a critical role to analyze vector time series, as they are needed for various purposes, especially to draw inference on the dependence…
The focus of modern biomedical studies has gradually shifted to explanation and estimation of joint effects of high dimensional predictors on disease risks. Quantifying uncertainty in these estimates may provide valuable insight into…
This paper proposes a desparsified GMM estimator for estimating high-dimensional regression models allowing for, but not requiring, many more endogenous regressors than observations. We provide finite sample upper bounds on the estimation…
We propose a high dimensional mean test framework for shrinking random variables, where the underlying random variables shrink to zero as the sample size increases. By pooling observations across overlapping subsets of dimensions, we…
Many statistical analyses involve the comparison of multiple data sets collected under different conditions in order to identify the difference in the underlying distributions. A common challenge in multi-sample comparison is the presence…