Related papers: High Dimensional Tests Based on U-Statistics for G…
To assess whether there is some signal in a big database, aggregate tests for the global null hypothesis of no effect are routinely applied in practice before more specialized analysis is carried out. Although a plethora of aggregate tests…
Motivated by the likelihood ratio test under the Gaussian assumption, we develop a maximum sum-of-squares test for conducting hypothesis testing on high dimensional mean vector. The proposed test which incorporates the dependence among the…
Generalized linear statistics are an unifying class that contains U-statistics, U-quantiles, L-statistics as well as trimmed and winsorized U-statistics. For example, many commonly used estimators of scale fall into this class.…
This paper considers testing linear hypotheses of a set of mean vectors with unequal covariance matrices in large dimensional setting. The problem of testing the hypothesis $H_0 : \sum_{i=1}^q \beta_i \bmu_i =\bmu_0 $ for a given vector…
Recently, several authors have re-examined the power of the classical F-test in linear regression in a `large-p, large-n' framework (cf. Zhong and Chen (2011), Wang and Cui (2013)). They highlight the loss of power as the number of…
A common problem in genetics is that of testing whether a set of highly dependent gene expressions differ between two populations, typically in a high-dimensional setting where the data dimension is larger than the sample size. Most…
We propose a new testing procedure of heteroskedasticity in high-dimensional linear regression, where the number of covariates can be larger than the sample size. Our testing procedure is based on residuals of the Lasso. We demonstrate that…
Nonparametric two sample testing deals with the question of consistently deciding if two distributions are different, given samples from both, without making any parametric assumptions about the form of the distributions. The current…
Many statistical methodologies for high-dimensional data assume the population is normal. Although a few multivariate normality tests have been proposed, to the best of our knowledge, none of them can properly control the type I error when…
In this paper, we investigate hypothesis testing for the linear combination of mean vectors across multiple populations through the method of random integration. We have established the asymptotic distributions of the test statistics under…
This paper is devoted to the study of the general linear hypothesis testing (GLHT) problem of multi-sample high-dimensional mean vectors. For the GLHT problem, we introduce a test statistic based on $L^2$-norm and random integration method,…
After variable selection, standard inferential procedures for regression parameters may not be uniformly valid; there is no finite-sample size at which a standard test is guaranteed to approximately attain its nominal size. This problem is…
This paper proposes a novel test method for high-dimensional mean testing regard for the temporal dependent data. Comparison to existing methods, we establish the asymptotic normality of the test statistic without relying on restrictive…
We prove a convergence theorem for U-statistics of degree two, where the data dimension $d$ is allowed to scale with sample size $n$. We find that the limiting distribution of a U-statistic undergoes a phase transition from the…
This paper studies inference for the mean vector of a high-dimensional $U$-statistic. In the era of Big Data, the dimension $d$ of the $U$-statistic and the sample size $n$ of the observations tend to be both large, and the computation of…
In this paper new tests for the independence of two high-dimensional vectors are investigated. We consider the case where the dimension of the vectors increases with the sample size and propose multivariate analysis of variance-type…
This article considers change point testing and estimation for a sequence of high-dimensional data. In the case of testing for a mean shift for high-dimensional independent data, we propose a new test which is based on $U$-statistic in Chen…
In this paper, we study the problem of testing the mean vectors of high dimensional data in both one-sample and two-sample cases. The proposed testing procedures employ maximum-type statistics and the parametric bootstrap techniques to…
Permutation testing in linear models, where the number of nuisance coefficients is smaller than the sample size, is a well-studied topic. The common approach of such tests is to permute residuals after regressing on the nuisance covariates.…
So-called linear rank statistics provide a means for distribution-free (even in finite samples), yet highly flexible, two-sample testing in the setting of univariate random variables. Their flexibility derives from a choice of weights that…