Group Inference in High Dimensions with Applications to Hierarchical Testing

09/04/2019
by   Zijian Guo, et al.
0

Group inference has been a long-standing question in statistics and the development of high-dimensional group inference is an essential part of statistical methods for analyzing complex data sets, including hierarchical testing, tests of interaction, detection of heterogeneous treatment effects and local heritability. Group inference in regression models can be measured with respect to a weighted quadratic functional of the regression sub-vector corresponding to the group. Asymptotically unbiased estimators of these weighted quadratic functionals are constructed and a procedure using these estimator for inference is proposed. We derive its asymptotic Gaussian distribution which allows to construct asymptotically valid confidence intervals and tests which perform well in terms of length or power. The results simultaneously address four challenges encountered in the literature: controlling coverage or type I error even when the variables inside the group are highly correlated, achieving a good power when there are many small coefficients inside the group, computational efficiency even for a large group, and no requirements on the group size. We apply the methodology to several interesting statistical problems and demonstrate its strength and usefulness on simulated and real data.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
01/25/2023

Statistical Inference and Large-scale Multiple Testing for High-dimensional Regression Models

This paper presents a selective survey of recent developments in statist...
research
02/21/2022

Statistical Inference for Genetic Relatedness Based on High-Dimensional Logistic Regression

This paper studies the problem of statistical inference for genetic rela...
research
01/06/2023

Rank-transformed subsampling: inference for multiple data splitting and exchangeable p-values

Many testing problems are readily amenable to randomised tests such as t...
research
07/24/2023

More Power by using Fewer Permutations

We consider testing invariance of a distribution under an algebraic grou...
research
09/22/2016

Robust Confidence Intervals in High-Dimensional Left-Censored Regression

This paper develops robust confidence intervals in high-dimensional and ...
research
06/05/2016

Statistical Inference for Algorithmic Leveraging

The age of big data has produced data sets that are computationally expe...
research
06/20/2020

Improving the replicability of results from a single psychological experiment

We identify two aspects of selective inference as major obstacles for re...

Please sign up or login with your details

Forgot password? Click here to reset