Related papers: A One-Sample Test for Normality with Kernel Method…
Modern large-scale kernel-based tests such as maximum mean discrepancy (MMD) and kernelized Stein discrepancy (KSD) optimize kernel hyperparameters on a held-out sample via data splitting to obtain the most powerful test statistics. While…
In this article, we propose a new class of consistent tests for $p$-variate normality. These tests are based on the characterization of the standard multivariate normal distribution, that the Hessian of the corresponding cumulant generating…
There exist a number of tests for assessing the nonparametric heteroscedastic location-scale assumption. Here we consider a goodness-of-fit test for the more general hypothesis of the validity of this model under a parametric functional…
Kernel methods have been among the most popular techniques in machine learning, where learning tasks are solved using the property of reproducing kernel Hilbert space (RKHS). In this paper, we propose a novel data analysis framework with…
Reproducing kernel Hilbert spaces (RKHSs) are special Hilbert spaces where all the evaluation functionals are linear and bounded. They are in one-to-one correspondence with positive definite maps called kernels. Stable RKHSs enjoy the…
We propose a new family of specification tests called kernel conditional moment (KCM) tests. Our tests are built on a novel representation of conditional moment restrictions in a reproducing kernel Hilbert space (RKHS) called conditional…
Testing the dependency between two random variables is an important inference problem in statistics since many statistical procedures rely on the assumption that the two samples are independent. To test whether two samples are independent,…
In this paper, we present the general theory of embedding independence tests on Hilbert spaces that generalizes the concepts of distance covariance, distance multivariance and HSIC. This is done by defining new types of kernel on an $n$…
The Gaussian graphical model is routinely employed to model the joint distribution of multiple random variables. The graph it induces is not only useful for describing the relationship between random variables but also critical for…
This paper introduces an approach for detecting differences in the first-order structures of spatial point patterns. The proposed approach leverages the kernel mean embedding in a novel way by introducing its approximate version tailored to…
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…
We propose an independence test for random variables valued into metric spaces by using a test statistic obtained from appropriately centering and rescaling the squared Hilbert-Schmidt norm of the usual empirical estimator of normalized…
The network data has attracted considerable attention in modern statistics. In research on complex network data, one key issue is finding its underlying connection structure given a network sample. The methods that have been proposed in…
Finite mixtures of multivariate normal distributions have been widely used in empirical applications in diverse fields such as statistical genetics and statistical finance. Testing the number of components in multivariate normal mixture…
In this paper, we propose a general method for testing inequality restrictions on nonparametric functions. Our framework includes many nonparametric testing problems in a unified framework, with a number of possible applications in auction…
A family of maximum mean discrepancy (MMD) kernel two-sample tests is introduced. Members of the test family are called Block-tests or B-tests, since the test statistic is an average over MMDs computed on subsets of the samples. The choice…
We develop methodology for testing hypotheses regarding the slope function in functional linear regression for time series via a reproducing kernel Hilbert space approach. In contrast to most of the literature, which considers tests for the…
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…
This paper studies convergence of empirical risks in reproducing kernel Hilbert spaces (RKHS). A conventional assumption in the existing research is that empirical training data do not contain any noise but this may not be satisfied in some…
In this article, we introduce a novel discrepancy called the maximum variance discrepancy for the purpose of measuring the difference between two distributions in Hilbert spaces that cannot be found via the maximum mean discrepancy. We also…