Related papers: Test for a Mean Vector with Fixed or Divergent Dim…
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,…
In this paper, we propose a test for the equality of multiple distributions based on kernel mean embeddings. Our framework provides a flexible way to handle multivariate or even high-dimensional data by virtue of kernel methods and allows…
High-dimensional data, where the dimension of the feature space is much larger than sample size, arise in a number of statistical applications. In this context, we construct the generalized multivariate sign transformation, defined as a…
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…
This paper provides a framework for estimating the mean and variance of a high-dimensional normal density. The main setting considered is a fixed number of vector following a high-dimensional normal distribution with unknown mean and…
We propose two families of tests for the classical goodness-of-fit problem to univariate normality. The new procedures are based on $L^2$-distances of the empirical zero-bias transformation to the normal distribution or the empirical…
The Wilcoxon signed-rank test and the Wilcoxon-Mann-Whitney test are commonly employed in one sample and two sample mean tests for one-dimensional hypothesis problems. For high-dimensional mean test problems, we calculate the asymptotic…
Change point testing for high-dimensional data has attracted a lot of attention in statistics and machine learning owing to the emergence of high-dimensional data with structural breaks from many fields. In practice, when the dimension is…
For a set of dependent random variables, without stationary or the strong mixing assumptions, we derive the asymptotic independence between their sums and maxima. Then we apply this result to high-dimensional testing problems, where we…
Limit distributions of likelihood ratio statistics are well-known to be discontinuous in the presence of nuisance parameters at the boundary of the parameter space, which lead to size distortions when standard critical values are used for…
The log-normal distribution is used to describe the positive data, that it has skewed distribution with small mean and large variance. This distribution has application in many sciences for example medicine, economics, biology and…
Metric mean dimension is a metric-depedent quantity to characterize the topological complexity of systems with infinite topological entropy. In this paper, we investigate metric mean dimension of factor maps. (1) We introduce three types of…
This paper explores hypothesis testing for the parametric forms of the mean and variance functions in regression models under diverging-dimension settings. To mitigate the curse of dimensionality, we introduce weighted residual empirical…
We propose a test for a change in the mean for a sequence of functional observations that are only partially observed on subsets of the domain, with no information available on the complement. The framework accommodates important scenarios,…
High-dimensional tests are applied to find relevant sets of variables and relevant models. If variables are selected by analyzing the sums of products matrices and a corresponding mean-value test is performed, there is the danger that the…
The statistical analysis of discrete data has been the subject of extensive statistical research dating back to the work of Pearson. In this survey we review some recently developed methods for testing hypotheses about high-dimensional…
The log-normal distribution is one of the most common distributions used for modeling skewed and positive data. It frequently arises in many disciplines of science, specially in the biological and medical sciences. The statistical analysis…
We introduce a new framework for the mean-variance spanning (MVS) hypothesis testing. The procedure can be applied to any test-asset dimension and only requires stationary asset returns and the number of benchmark assets to be smaller than…
Popular measures of meta-analysis heterogeneity, such as $I^2$, cannot be considered measures of population heterogeneity since they are dependant on samples sizes within studies. The coefficient of variation (CV) recently introduced and…
The testing-based approach is a fundamental tool for establishing posterior contraction rates. Although the Hellinger metric is attractive owing to the existence of a desirable test function, it is not directly applicable in Gaussian…