Related papers: Testing hypotheses about mixture distributions usi…
Model checking plays an important role in linear regression as model misspecification seriously affects the validity and efficiency of regression analysis. In practice, model checking is often performed by subjectively evaluating the plot…
We consider the problem of testing whether pairs of univariate random variables are associated. Few tests of independence exist that are consistent against all dependent alternatives and are distribution free. We propose novel tests that…
Given n observations, we study the consistency of a batch of k new observations, in terms of their distribution function. We propose a non-parametric, non-likelihood test based on Edgeworth expansion of the distribution function. The…
Two new goodness of fit tests for the Pareto type-I distribution for complete and right censored data are proposed using fixed point characterization based on Steins type identity. The asymptotic distributions of the test statistics under…
We introduce a new characterization of Pareto distribution and construct integral and supremum type goodness-of-fit tests based on it. Limiting distribution and large deviations of new statistics are described and their local Bahadur…
We propose several statistics to test the Markov hypothesis for $\beta$-mixing stationary processes sampled at discrete time intervals. Our tests are based on the Chapman--Kolmogorov equation. We establish the asymptotic null distributions…
We study the problem of testing discrete distributions with a focus on the high probability regime. Specifically, given samples from one or more discrete distributions, a property $\mathcal{P}$, and parameters $0< \epsilon, \delta <1$, we…
Distributed frameworks are widely used to handle massive data, where sample size $n$ is very large, and data are often stored in $k$ different machines. For a random vector $X\in \mathbb{R}^p$ with expectation $\mu$, testing the mean vector…
A framework is developed using techniques from rate distortion theory in statistical testing. The idea is first to do optimal compression according to a certain distortion function and then use information divergence from the compressed…
The asymptotically optimal hypothesis testing problem with the general sources as the null and alternative hypotheses is studied under exponential-type error constraints on the first kind of error probability. Our fundamental philosophy in…
The hypothesis of randomness is fundamental in statistical machine learning and in many areas of nonparametric statistics; it says that the observations are assumed to be independent and coming from the same unknown probability…
We consider goodness-of-fit tests of symmetric stable distributions based on weighted integrals of the squared distance between the empirical characteristic function of the standardized data and the characteristic function of the standard…
We use a Stein identity to define a new class of parametric distributions which we call ``independent additive weighted bias distributions.'' We investigate related $L^2$-type discrepancy measures, empirical versions of which not only…
We develop here several goodness-of-fit tests for testing the k-monotonicity of a discrete density, based on the empirical distribution of the observations. Our tests are non-parametric, easy to implement and are proved to be asymptotically…
We consider the problem of testing whether two finite-dimensional random dot product graphs have generating latent positions that are independently drawn from the same distribution, or distributions that are related via scaling or…
This paper presents and examines computationally convenient goodness-of-fit tests for the family of generalized Poisson distributions, which encompasses notable distributions such as the Compound Poisson and the Katz distributions. The…
The bivariate Poisson distribution is commonly used to model bivariate count data. In this paper we study a goodness-of-fit test for this distribution. We also provide a review of the existing tests for the bivariate Poisson distribution,…
Test of independence is of fundamental importance in modern data analysis, with broad applications in variable selection, graphical models, and causal inference. When the data is high dimensional and the potential dependence signal is…
This paper investigates the problem of testing independence of two random vectors of general dimensions. For this, we give for the first time a distribution-free consistent test. Our approach combines distance covariance with the…
By extrapolating the explicit formula of the zero-bias distribution occurring in the context of Stein's method, we construct characterization identities for a large class of absolutely continuous univariate distributions. Instead of trying…