Related papers: P-values for high-dimensional regression
We introduce the notion of p*-values (p*-variables), which generalizes p-values (p-variables) in several senses. The new notion has four natural interpretations: operational, probabilistic, Bayesian, and frequentist. A main example of a…
The PC algorithm allows investigators to estimate a complete partially directed acyclic graph (CPDAG) from a finite dataset, but few groups have investigated strategies for estimating and controlling the false discovery rate (FDR) of the…
Statistical significance of both the original and the replication study is a commonly used criterion to assess replication attempts, also known as the two-trials rule in drug development. However, replication studies are sometimes conducted…
In this paper, we are concerned with how to select significant variables in semiparametric modeling. Variable selection for semiparametric regression models consists of two components: model selection for nonparametric components and…
This paper aims to propose and theoretically analyze a new distributed scheme for sparse linear regression and feature selection. The primary goal is to learn the few causal features of a high-dimensional dataset based on noisy observations…
We introduce a joint posterior $p$-value, an extension of the posterior predictive $p$-value for multiple test statistics, designed to address limitations of existing Bayesian $p$-values in the setting of continuous model expansion. In…
We present a mathematically justifiable, computationally simple, sample eigenvalue based procedure for estimating the number of high-dimensional signals in white noise using relatively few samples. The main motivation for considering a…
Examining residuals such as Pearson and deviance residuals, is a standard tool for assessing normal regression. However, for discrete response, these residuals cluster on lines corresponding to distinct response values. Their distributions…
Large sample size brings the computation bottleneck for modern data analysis. Subsampling is one of efficient strategies to handle this problem. In previous studies, researchers make more fo- cus on subsampling with replacement (SSR) than…
In probabilistic logic entailments, even moderate size problems can yield linear constraint systems with so many variables that exact methods are impractical. This difficulty can be remedied in many cases of interest by introducing a three…
Permutation tests are amongst the most commonly used statistical tools in modern genomic research, a process by which p-values are attached to a test statistic by randomly permuting the sample or gene labels. Yet permutation p-values…
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 chapter demystifies P-values, hypothesis tests and significance tests, and introduces the concepts of local evidence and global error rates. The local evidence is embodied in \textit{this} data and concerns the hypotheses of interest…
This paper proposes a new algorithm for multiple sparse regression in high dimensions, where the task is to estimate the support and values of several (typically related) sparse vectors from a few noisy linear measurements. Our algorithm is…
We are concerned with multiple test problems with composite null hypotheses and the estimation of the proportion $\pi_{0}$ of true null hypotheses. The Schweder-Spj\o tvoll estimator $\hat{\pi}_0$ utilizes marginal $p$-values and only works…
Threshold selection plays a key role for various aspects of statistical inference of rare events. Most classical approaches tackling this problem for heavy-tailed distributions crucially depend on tuning parameters or critical values to be…
In this paper, we construct the wavelet eigenvalue regression methodology in high dimensions. We assume that possibly non-Gaussian, finite-variance $p$-variate measurements are made of a low-dimensional $r$-variate ($r \ll p$) fractional…
Researchers now routinely use AI or other machine learning methods to estimate latent variables of economic interest, then plug-in the estimates as covariates in a regression. We show both theoretically and empirically that naively treating…
Combining p-values from independent statistical tests is a popular approach to meta-analysis, particularly when the data underlying the tests are either no longer available or are difficult to combine. A diverse range of p-value combination…
Variance estimation is a fundamental problem in statistical modeling. In ultrahigh dimensional linear regressions where the dimensionality is much larger than sample size, traditional variance estimation techniques are not applicable.…