Related papers: A Note on High Dimensional Two Sample Mean Test
Testing heteroscedasticity of the errors is a major challenge in high-dimensional regressions where the number of covariates is large compared to the sample size. Traditional procedures such as the White and the Breusch-Pagan tests…
We propose the density ratio permutation test, a hypothesis test that assesses whether the ratio between two densities is proportional to a known function based on independent samples from each distribution. The test uses an efficient…
We discuss the recently discovered two-dimensional metal-insulator transition in zero magnetic field in the light of the scaling theory of localization. We demonstrate that the observed symmetry relating conductivity and resistivity follows…
This paper investigates the problem of detecting relevant change points in the mean vector, say $\mu_t =(\mu_{1,t},\ldots ,\mu_{d,t})^T$ of a high dimensional time series $(Z_t)_{t\in \mathbb{Z}}$. While the recent literature on testing for…
Extending to dimension 2 and higher the dual univariate concepts of ranks and quantiles has remained an open problem for more than half a century. Based on measure transportation results, a solution has been proposed recently under the name…
The problem of testing changes in covariance has received increasing attention in recent years, especially in the context of high-dimensional testing. A number of approaches have been proposed, all limited to the two-sample problem and…
In this paper, we study inference for high-dimensional data characterized by small sample sizes relative to the dimension of the data. In particular, we provide an infinite-dimensional framework to study statistical models that involve…
Repeated observations have become increasingly common in biomedical research and longitudinal studies. For instance, wearable sensor devices are deployed to continuously track physiological and biological signals from each individual over…
New inference methods for the multivariate coefficient of variation and its reciprocal, the standardized mean, are presented. While there are various testing procedures for both parameters in the univariate case, it is less known how to do…
In this paper, we propose a new test for checking the parametric form of the conditional variance based on distance covariance in nonlinear and nonparametric regression models. Inherit from the nice properties of distance covariance, our…
We study a high-dimensional regression setting under the assumption of known covariate distribution. We aim at estimating the amount of explained variation in the response by the best linear function of the covariates (the signal level). In…
Testing mutual independence among multiple random variables is a fundamental problem in statistics, with wide applications in genomics, finance, and neuroscience. In this paper, we propose a new class of tests for high-dimensional mutual…
In this work, we generalize the Cram\'er-von Mises statistic via projection-averaging to obtain a robust test for the multivariate two-sample problem. The proposed test is consistent against all fixed alternatives, robust to heavy-tailed…
High-dimensional logistic regression is widely used in analyzing data with binary outcomes. In this paper, global testing and large-scale multiple testing for the regression coefficients are considered in both single- and two-regression…
Information from related source studies can often enhance the findings of a target study. However, the distribution shift between target and source studies can severely impact the efficiency of knowledge transfer. In the high-dimensional…
In many real-world applications, it is common that a proportion of the data may be missing or only partially observed. We develop a novel two-sample testing method based on the Maximum Mean Discrepancy (MMD) which accounts for missing data…
The Maximum Mean Discrepancy (MMD) is a widely used multivariate distance metric for two-sample testing. The standard MMD test statistic has an intractable null distribution typically requiring costly resampling or permutation approaches…
We present an algorithm for testing halfspaces over arbitrary, unknown rotation-invariant distributions. Using $\tilde O(\sqrt{n}\epsilon^{-7})$ random examples of an unknown function $f$, the algorithm determines with high probability…
This paper proposes new tests of conditional independence of two random variables given a single-index involving an unknown finite-dimensional parameter. The tests employ Rosenblatt transforms and are shown to be distribution-free while…
Modern statistical analysis often encounters high dimensional models but with limited sample sizes. This makes the target data based statistical estimation very difficult. Then how to borrow information from another large sized source data…