Related papers: Asymptotics and practical aspects of testing norma…

A Hilbert space embedding of a distribution---in short, a kernel mean embedding---has recently emerged as a powerful tool for machine learning and inference. The basic idea behind this framework is to map distributions into a reproducing…

We establish sufficient conditions for the asymptotic normality of kernel density estimators, applied to causal linear random fields. Our conditions on the coefficients of linear random fields are weaker than known results, although our…

The asymptotic solution to the problem of comparing the means of two heteroscedastic populations, based on two random samples from the populations, hinges on the pivot underpinning the construction of the confidence interval and the test…

A Hilbert space embedding for probability measures has recently been proposed, with applications including dimensionality reduction, homogeneity testing, and independence testing. This embedding represents any probability measure as a mean…

We establish the asymptotic normality of the kernel type estimator for the regression function constructed from quasi-associated data when the explanatory variable takes its values in a separable Hilbert space.

We consider covariance parameter estimation for Gaussian processes with functional inputs. From an increasing-domain asymptotics perspective, we prove the asymptotic consistency and normality of the maximum likelihood estimator. We extend…

The object of study is the problem of testing for uniformity of the multinomial distribution. We consider tests based on symmetric statistics, defined as the sum of some function of cell-frequencies. Mainly, attention is focused on the…

Two new test statistics are introduced to test the null hypotheses that the sampling distribution has an increasing hazard rate on a specified interval [0,a]. These statistics are empirical L_1-type distances between the isotonic estimates,…

We introduce a kernel-based two-sample test for comparing probability distributions up to group actions. Our construction yields invariant kernels for locally compact $\sigma$-compact groups and extends classical Haar-based approaches…

Over the last decade, an approach that has gained a lot of popularity to tackle nonparametric testing problems on general (i.e., non-Euclidean) domains is based on the notion of reproducing kernel Hilbert space (RKHS) embedding of…

We propose a novel kernel-based two-sample test that leverages the spectral decomposition of the maximum mean discrepancy (MMD) statistic to identify and utilize well-estimated directional components in reproducing kernel Hilbert space…

We propose a kernel-based partial permutation test for checking the equality of functional relationship between response and covariates among different groups. The main idea, which is intuitive and easy to implement, is to keep the…

The large-sample behavior of non-degenerate multivariate $U$-statistics of arbitrary degree is investigated under the assumption that their kernel depends on parameters that can be estimated consistently. Mild regularity conditions are…

Kernel methods, being supported by a well-developed theory and coming with efficient algorithms, are among the most popular and successful machine learning techniques. From a mathematical point of view, these methods rest on the concept of…

We propose a nonparametric statistical test for goodness-of-fit: given a set of samples, the test determines how likely it is that these were generated from a target density function. The measure of goodness-of-fit is a divergence…

Kernel mean embeddings are a popular tool that consists in representing probability measures by their infinite-dimensional mean embeddings in a reproducing kernel Hilbert space. When the kernel is characteristic, mean embeddings can be used…

The kernel two-sample test based on the maximum mean discrepancy (MMD) is one of the most popular methods for detecting differences between two distributions over general metric spaces. In this paper we propose a method to boost the power…

Are two sets of observations drawn from the same distribution? This problem is a two-sample test. Kernel methods lead to many appealing properties. Indeed state-of-the-art approaches use the $L^2$ distance between kernel-based distribution…

We derive the joint asymptotic distribution of empirical quantiles and expected shortfalls under general conditions on the distribution of the underlying observations. In particular, we do not assume that the distribution function is…

In this paper, a Bayesian semiparametric copula approach is used to model the underlying multivariate distribution $F_{true}$. First, the Dirichlet process is constructed on the unknown marginal distributions of $F_{true}$. Then a Gaussian…