Related papers: A Flexible Framework for Hypothesis Testing in Hig…
Scalar-on-function linear models are commonly used to regress functional predictors on a scalar response. However, functional models are more difficult to estimate and interpret than traditional linear models, and may be unnecessarily…
Statistical inferences for high-dimensional regression models have been extensively studied for their wide applications ranging from genomics, neuroscience, to economics. However, in practice, there are often potential unmeasured…
We investigate the problem of testing the global null in the high-dimensional regression models when the feature dimension $p$ grows proportionally to the number of observations $n$. Despite a number of prior work studying this problem,…
In this paper, we propose a general method for testing composite hypotheses. Our idea is to use confidence limits to define stopping and decision rules. The requirements of operating characteristic function can be satisfied by adjusting the…
High-dimensional vector autoregression with measurement error is frequently encountered in a large variety of scientific and business applications. In this article, we study statistical inference of the transition matrix under this model.…
A framework for estimation and hypothesis testing of functional restrictions against general alternatives is proposed. The parameter space is a reproducing kernel Hilbert space (RKHS). The null hypothesis does not necessarily define a…
We propose a hypothesis test that allows for many tested restrictions in a heteroskedastic linear regression model. The test compares the conventional F statistic to a critical value that corrects for many restrictions and conditional…
Many methods have been developed to estimate the set of relevant variables in a sparse linear model Y= XB+e where the dimension p of B can be much higher than the length n of Y. Here we propose two new methods based on multiple hypotheses…
This paper proposes a novel two-step strategy for testing the goodness-of-fit of parametric regression models in ultra-high dimensional sparse settings, where the predictor dimension far exceeds the sample size. This regime usually renders…
In this paper, we have established a general framework of multistage hypothesis tests which applies to arbitrarily many mutually exclusive and exhaustive composite hypotheses. Within the new framework, we have constructed specific…
In this paper, we present a general framework for testing relevant hypotheses in functional time series. Our unified approach covers one-sample, two-sample, and change point problems under contaminated observations with arbitrary sampling…
The issue addressed in this paper is that of testing for common breaks across or within equations of a multivariate system. Our framework is very general and allows integrated regressors and trends as well as stationary regressors. The null…
A simple test is proposed for examining the correctness of a given completely specified response function against unspecified general alternatives in the context of univariate regression. The usual diagnostic tools based on residuals plots…
This paper develops an approach to inference in a linear regression model when the number of potential explanatory variables is larger than the sample size. The approach treats each regression coefficient in turn as the interest parameter,…
We propose new methods for multivariate linear regression when the regression coefficient matrix is sparse and the error covariance matrix is dense. We assume that the error covariance matrix has equicorrelation across the response…
Score-based statistical models play an important role in modern machine learning, statistics, and signal processing. For hypothesis testing, a score-based hypothesis test is proposed in \cite{wu2022score}. We analyze the performance of this…
Consider a high-dimensional linear regression problem, where the number of covariates is larger than the number of observations and the interest is in estimating the conditional variance of the response variable given the covariates. A…
We consider high-dimensional generalized linear models when the covariates are contaminated by measurement error. Estimates from errors-in-variables regression models are well-known to be biased in traditional low-dimensional settings if…
The classical binary hypothesis testing problem is revisited. We notice that when one of the hypotheses is composite, there is an inherent difficulty in defining an optimality criterion that is both informative and well-justified. For…
Heteroscedasticity testing is of importance in regression analysis. Existing local smoothing tests suffer severely from curse of dimensionality even when the number of covariates is moderate because of use of nonparametric estimation. In…