Related papers: Significance Testing and Group Variable Selection
In this paper, we propose a novel approach to test the equality of high-dimensional mean vectors of several populations via the weighted $L_2$-norm. We establish the asymptotic normality of the test statistics under the null hypothesis. We…
In the analysis of survival outcome supplemented with both clinical information and high-dimensional gene expression data, use of the traditional Cox proportional hazards model (1972) fails to meet some emerging needs in biomedical…
Variable selection plays an important role in the high-dimensional data analysis. However the high-dimensional data often induces the strongly correlated variables problem. In this paper, we propose Elastic Net procedure for partially…
In many scientific and engineering applications, covariates are naturally grouped. When the group structures are available among covariates, people are usually interested in identifying both important groups and important variables within…
The generalized likelihood ratio (GLR) test proposed by Fan, Zhang and Zhang [Ann. Statist. 29 (2001) 153-193] and Fan and Yao [Nonlinear Time Series: Nonparametric and Parametric Methods (2003) Springer] is a generally applicable…
The American Statistical Association (ASA) statement on statistical significance and P-values \cite{wasserstein2016asa} cautioned statisticians against making scientific decisions solely on the basis of traditional P-values. The statement…
We propose a new Gini correlation to measure dependence between a categorical and numerical variables. Analogous to Pearson $R^2$ in ANOVA model, the Gini correlation is interpreted as the ratio of the between-group variation and the total…
Permutation tests are a distribution free way of performing hypothesis tests. These tests rely on the condition that the observed data are exchangeable among the groups being tested under the null hypothesis. This assumption is easily…
It is of importance to investigate the significance of a subset of covariates $W$ for the response $Y$ given covariates $Z$ in regression modeling. To this end, we propose a significance test for the partial mean independence problem based…
We propose a test of many zero parameter restrictions in a high dimensional linear iid regression model with $k$ $>>$ $n$ regressors. The test statistic is formed by estimating key parameters one at a time based on many low dimension…
Causal effect estimation is a critical task in statistical learning that aims to find the causal effect on subjects by identifying causal links between a number of predictor (or, explanatory) variables and the outcome of a treatment. In a…
We develop a pivotal test to assess the statistical significance of the feature variables in a single-layer feedforward neural network regression model. We propose a gradient-based test statistic and study its asymptotics using…
We develop non-asymptotically justified methods for hypothesis testing about the $p-$dimensional coefficients $\theta^{*}$ in (possibly nonlinear) regression models. Given a function $h:\,\mathbb{R}^{p}\mapsto\mathbb{R}^{m}$, we consider…
In an observational study, it is common to leverage known null effect to detect bias. One such strategy is to set aside a placebo sample -- a subset of data immune from the hypothesized cause-and-effect relationship. Existence of an effect…
Variable selection has become a pivotal choice in data analyses that impacts subsequent inference and prediction. In linear models, variable selection using Second-Generation P-Values (SGPV) has been shown to be as good as any other…
Considering a regression model, we address the question of testing the nullity of the regression function. The testing procedure is available when the variance of the observations is unknown and does not depend on any prior information on…
We propose the variable selection procedure incorporating prior constraint information into lasso. The proposed procedure combines the sample and prior information, and selects significant variables for responses in a narrower region where…
Model checking plays an important role in linear regression as model misspecification seriously affects the validity and efficiency of regression analysis. In practice, model checking is often performed by subjectively evaluating the plot…
An important feature of linear mixed models and generalized linear mixed models is that the conditional mean of the response given the random effects, after transformed by a link function, is linearly related to the fixed covariate effects…
We propose a Bayesian variable selection method in the framework of modal regression for heavy-tailed responses. An efficient expectation-maximization algorithm is employed to expedite parameter estimation. A test statistic is constructed…