Related papers: Optimal tests for elliptical symmetry: specified a…
This paper develops several interesting, significant, and interconnected approaches to nonparametric or semi-parametric statistical inferences. The overwhelmingly favoured maximum likelihood estimator (MLE) under parametric model is…
Principled nonparametric tests for regression curvature in $\mathbb{R}^{d}$ are often statistically and computationally challenging. This paper introduces the stratified incomplete local simplex (SILS) tests for joint concavity of…
Characteristic-function based goodness-of-fit tests are suggested for multivariate observations. The test statistics, which are straightforward to compute, are defined as two-sample criteria measuring discrepancy between multivariate ranks…
In this paper, we consider the sphericity test for a one-sample problem under high-dimensional two-step monotone incomplete data. Existing asymptotic expansions for the null distributions of the likelihood ratio test (LRT) statistic and…
Using fixed point characterization, we develop a new goodness of fit test for uniform distribution. We also discuss how the right censored observations can be incorporated in the proposed test procedure. We study the asymptotic properties…
Random geometric graphs are widely used in modeling geometry and dependence structure in networks. In a random geometric graph, nodes are independently generated from some probability distribution $F$ over a metric space, and edges link…
We establish higher-order nonasymptotic expansions for a difference between probability distributions of sums of i.i.d. random vectors in a Euclidean space. The derived bounds are uniform over two classes of sets: the set of all Euclidean…
We propose a new $L^2$-type goodness-of-fit test for the family of beta distributions based on a conditional moment characterisation. The asymptotic null distribution is identified, and since it depends on the underlying parameters, a…
This paper introduces a quasi-likelihood ratio testing procedure for diffusion processes observed under nonsynchronous sampling schemes. High-frequency data, particularly in financial econometrics, are often recorded at irregular time…
Testing hypotheses of goodness-of-fit about mixture distributions on the basis of independent but not necessarily identically distributed random vectors is considered. The hypotheses are given by a specific distribution or by a family of…
The sign test (Arbuthnott, 1710) and the Wilcoxon signed-rank test (Wilcoxon, 1945) are among the first examples of a nonparametric test. These procedures -- based on signs, (absolute) ranks and signed-ranks -- yield distribution-free tests…
We discuss in this paper a possibility of constructing a whole class of asymptotic distribution-free tests for testing regularly varying tail distributions. The idea is that we treat the tails of distributions as members of a parametric…
We study a stylized multiple testing problem where the test statistics are independent and assumed to have the same distribution under their respective null hypotheses. We first show that, in the normal means model where the test statistics…
Elliptically symmetric distributions are a classic example of a semiparametric model where the location vector and the scatter matrix (or a parameterization of them) are the two finite-dimensional parameters of interest, while the density…
We study the problem of robustly estimating the mean or location parameter without moment assumptions. We show that for a large class of symmetric distributions, the same error as in the Gaussian setting can be achieved efficiently. The…
In this paper, we treat an asymptotic hypothesis testing (or state discrimination with asymmetric treatment of errors) between an arbitrary fixed bipartite pure state and the completely mixed state by one-way LOCC, two-way LOCC, and…
We consider a class of hypothesis testing problems where the null hypothesis postulates $M$ distributions for the observed data, and there is only one possible distribution under the alternative. We show that one can use a stochastic mirror…
A survey of goodness-of-fit and symmetry tests based on the characterization properties of distributions is presented. This approach became popular in recent years. In most cases the test statistics are functionals of $U$-empirical…
Given the probability measure $\nu$ over the given region $\Omega\subset \R^n$, we consider the optimal location of a set $\Sigma$ composed by $n$ points $\Om$ in order to minimize the average distance $\Sigma\mapsto \int_\Om…
Many scientific applications involve testing theories that are only partially specified. This task often amounts to testing the goodness-of-fit of a candidate distribution while allowing for reasonable deviations from it. The tolerant…