Related papers: Two-sample test based on maximum variance discrepa…
We characterize the asymptotic performance of nonparametric goodness of fit testing. The exponential decay rate of the type-II error probability is used as the asymptotic performance metric, and a test is optimal if it achieves the maximum…
Data depth has been applied as a nonparametric measurement for ranking multivariate samples. In this paper, we focus on homogeneity tests to assess whether two multivariate samples are from the same distribution. There are many data…
We define two minimum distance estimators for dependent data by minimizing some approximated Maximum Mean Discrepancy distances between the true empirical distribution of observations and their assumed (parametric) model distribution. When…
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…
Two-sample testing is a fundamental problem in statistics. Despite its long history, there has been renewed interest in this problem with the advent of high-dimensional and complex data. Specifically, in the machine learning literature,…
We propose a new nonparametric test for the supposition of independence between two continuous random variables. The test is based on the size of the longest increasing subsequence of a random permutation. We identified the independence…
We introduce estimation and test procedures through divergence optimization for discrete or continuous parametric models. This approach is based on a new dual representation for divergences. We treat point estimation and tests for simple…
We consider a linear regression model and propose an omnibus test to simultaneously check the assumption of independence between the error and the predictor variables, and the goodness-of-fit of the parametric model. Our approach is based…
The kernel Maximum Mean Discrepancy~(MMD) is a popular multivariate distance metric between distributions that has found utility in two-sample testing. The usual kernel-MMD test statistic is a degenerate U-statistic under the null, and thus…
Fitting mixture distributions is needed in applications where data belongs to inhomogeneous populations comprising homogeneous sub-populations. The mixing proportions of the sub populations are in general unknown and need to be estimated as…
We consider the problem of estimating the population probability distribution given a finite set of multivariate samples, using the maximum entropy approach. In strict keeping with Jaynes' original definition, our precise formulation of the…
In this paper, we propose two new tests for testing the equality of the covariance functions of several functional populations, namely a quasi GPF test and a quasi $F_{\max}$ test. The asymptotic random expressions of the two tests under…
Testing to see whether a given data set comes from some specified distribution is among the oldest types of problems in Statistics. Many such tests have been developed and their performance studied. The general result has been that while a…
We study strictly proper scoring rules in the Reproducing Kernel Hilbert Space. We propose a general Kernel Scoring rule and associated Kernel Divergence. We consider conditions under which the Kernel Score is strictly proper. We then…
In clinical and epidemiological research doubly truncated data often appear. This is the case, for instance, when the data registry is formed by interval sampling. Double truncation generally induces a sampling bias on the target variable,…
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…
We propose a new class of goodness-of-fit tests for the inverse Gaussian distribution. The proposed tests are weighted $L^2$-type tests depending on a tuning parameter. We develop the asymptotic theory under the null hypothesis and under a…
Maximum Variance Unfolding is one of the main methods for (nonlinear) dimensionality reduction. We study its large sample limit, providing specific rates of convergence under standard assumptions. We find that it is consistent when the…
It is well-known that in some situations it is not easy to compute the likelihood function as the datasets might be large or the model is too complex. In that contexts composite likelihood, derived by multiplying the likelihoods of subjects…
Under the null hypothesis, the marginal probability of the positive response is symmetric at any specified correlated coefficient, and the discordance probability is also symmetric to the positive response probability. The marginal…