Related papers: Comparison of Efficiencies of Symmetry Tests aroun…
We use a characterization of symmetry in terms of extremal order statistics which enables to build several new nonparametric tests of symmetry. We discuss their limiting distributions and calculate their local exact Bahadur efficiency under…
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…
Non-degenerate U-empirical Kolmogorov-Smirnov tests are studied and their large deviation asymptotics under the null-hypothesis is described. Several examples of such statistics used for testing goodness-of-fit and symmetry are considered.…
In this paper a new class of uniformity tests is proposed. It is shown that those tests are applicable to the cases of any simple null hypothesis as well as for the composite null hypothesis of rectangular distributions on arbitrary…
In this paper some well-known tests based on empirical distribution functions (EDF) with estimated parameters for testing composite normality hypothesis are revisited, and some new results on asymptotic properties are provided. In…
We introduce new test statistic to test the independence of two multi-dimensional random variables. Based on the $L_1$-distance and the historgram density estimation method, the test is compared via Bahadur relative efficiency to several…
Two new symmetry tests, of integral and Kolmogorov type, based on the characterization by squares of linear statistics are proposed. The test statistics are related to the family of degenerate U-statistics. Their asymptotic properties are…
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…
In this paper, we develop optimal tests for symmetry on the hyper-dimensional torus, leveraging Le Cam's methodology. We address both scenarios where the center of symmetry is known and where it is unknown. These tests are not only valid…
We review the alternative proposals introduced recently in the literature to update the standard formula to estimate the uncertainty on the mean of repeated measurements, and we compare their performances on synthetic examples with normal…
Parametric and semiparametric tests of circular reflective symmetry about an unknown central direction are developed that are locally and asymptotically optimal in the Le Cam sense against asymmetric $k$-sine-skewed alternatives. The…
In this paper, we are testing the symmetry in the distribution of data observed on a random variable. We proposed test statistics using cumulative past and residual extropy of record values based on the characterization developed by Gupta…
We revisit the problem of testing for multivariate reflected symmetry about an unspecified point. Although this testing problem is invariant with respect to full-rank affine transformations, among the hitherto few proposed tests only the…
We consider goodness-of-fit tests for uniformity of a multinomial distribution by means of tests based on a class of symmetric statistics, defined as the sum of some function of cell-frequencies. We are dealing with an asymptotic regime,…
Two new tests for exponentiality, of integral and Kolmogorov type, are proposed. They are based on a recent characterization and formed using appropriate V-statistics. Their asymptotic properties are examined and their local Bahadur…
A unified framework is proposed for tests of unobserved heterogeneity in parametric statistic models based on Neyman's $C(\alpha)$ approach. Such tests are irregular in the sense that the first order derivative of the log likelihood with…
We present a novel family of nonparametric omnibus tests of the hypothesis that two unknown but estimable functions are equal in distribution when applied to the observed data structure. We developed these tests, which represent a…
For a sequence of independent identically distributed random variables having a distribution function with an unknown parameter from a set $\Theta \subset \mathbf{R}^d$, we prove an analogue of the lower bound of Bahadur asymptotic…
Symmetry is an important and unifying notion in many areas of physics. In quantum mechanics, it is possible to eliminate degrees of freedom from a system by leveraging symmetry to identify the possible physical transitions. This allows us…
Given a random sample of observations, mixtures of normal densities are often used to estimate the unknown continuous distribution from which the data come. Here we propose the use of this semiparametric framework for testing symmetry about…