Related papers: Testability of high-dimensional linear models with…

This paper considers the problem of robust hypothesis testing under non-identically distributed data. We propose Wald-type tests for both simple and composite hypothesis for independent but non-homogeneous observations based on the robust…

A dimension reduction-based adaptive-to-model test is proposed for significance of a subset of covariates in the context of a nonparametric regression model. Unlike existing local smoothing significance tests, the new test behaves like a…

This article develops a framework for testing general hypothesis in high-dimensional models where the number of variables may far exceed the number of observations. Existing literature has considered less than a handful of hypotheses, such…

A novel framework is introduced to formalize identifiability in well-specified but ill-posed linear regression models. The framework is distribution-free and accommodates highly correlated features that may or may not relate to the…

Inference and prediction under the sparsity assumption have been a hot research topic in recent years. However, in practice, the sparsity assumption is difficult to test, and more importantly can usually be violated. In this paper, to study…

We study the detection of a change in the covariance matrix of $n$ independent sub-Gaussian random variables of dimension $p$. Our first contribution is to show that $\log\log(8n)$ is the exact minimax testing rate for a change in variance…

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 new test of heteroscedasticity for parametric regression models and partial linear regression models in high dimensional settings. When the dimension of covariates is large, existing tests of heteroscedasticity…

For the last two decades, high-dimensional data and methods have proliferated throughout the literature. Yet, the classical technique of linear regression has not lost its usefulness in applications. In fact, many high-dimensional…

Testing high-dimensional quantile regression coefficients is crucial, as tail quantiles often reveal more than the mean in many practical applications. Nevertheless, the sparsity pattern of the alternative hypothesis is typically unknown in…

This paper focuses on the problem of testing the null hypothesis that the regression functions of several populations are equal under a general nonparametric homoscedastic regression model. It is well known that linear kernel regression…

We derive a new class of statistical tests for generalized linear models based on thresholding point estimators. These tests can be employed whether the model includes more parameters than observations or not. For linear models, our tests…

Many inference techniques for multivariate data analysis assume that the rows of the data matrix are realizations of independent and identically distributed random vectors. Such an assumption will be met, for example, if the rows of the…

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…

For high-dimensional inference problems, statisticians have a number of competing interests. On the one hand, procedures should provide accurate estimation, reliable structure learning, and valid uncertainty quantification. On the other…

We consider the problem of testing whether pairs of univariate random variables are associated. Few tests of independence exist that are consistent against all dependent alternatives and are distribution free. We propose novel tests that…

In this paper, we consider tests for ultrahigh-dimensional partially linear regression models. The presence of ultrahigh-dimensional nuisance covariates and unknown nuisance function makes the inference problem very challenging. We adopt…

Statistical inference in high dimensional settings has recently attracted enormous attention within the literature. However, most published work focuses on the parametric linear regression problem. This paper considers an important…

We consider a nonlinear polynomial regression model in which we wish to test the null hypothesis of structural stability in the regression parameters against the alternative of a break at an unknown time. We derive the extreme value…

We show that when a high-dimensional data matrix is the sum of a low-rank matrix and a random error matrix with independent entries, the low-rank component can be consistently estimated by solving a convex minimization problem. We develop a…