Related papers: Student's t-test without symmetry conditions

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…

For any continuous zero-mean random variable (r.v.) X, a reciprocating function r is constructed, based only on the distribution of X, such that the conditional distribution of X given the (at-most-)two-point set {X,r(X)} is the zero-mean…

Symmetry plays a central role in the sciences, machine learning, and statistics. For situations in which data are known to obey a symmetry, a multitude of methods that exploit symmetry have been developed. Statistical tests for the presence…

We consider the problem of detecting sparse heterogeneous mixtures from a nonparametric perspective, and develop distribution-free tests when all effects have the same sign. Specifically, we assume that the null distribution is symmetric…

We consider Hotelling's T^2 statistic for an arbitrary d-dimensional sample. If the sampling is not too deterministic or inhomogeneous, then under zero means hypothesis, T^2 tends to \chi^2_d in distribution. We show that a test for the…

Symmetry plays a central role in the sciences, machine learning, and statistics. While statistical tests for the presence of distributional invariance with respect to groups have a long history, tests for conditional symmetry in the form of…

This paper presents a procedure for testing the hypothesis that the underlying distribution of the data is elliptical when using robust location and scatter estimators instead of the sample mean and covariance matrix. Under mild assumptions…

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…

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…

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…

The tails of the distribution of a mean zero, variance $\sigma^2$ random variable $Y$ satisfy concentration of measure inequalities of the form $\mathbb{P}(Y \ge t) \le \exp(-B(t))$ for $$ B(t)=\frac{t^2}{2( \sigma^2 + ct)} \quad \mbox{for…

Bayesian tests on the symmetry of the generalized von Mises model for planar directions (Gatto and Jammalamadaka, 2007) are introduced. The generalized von Mises distribution is a flexible model that can be axially symmetric or asymmetric,…

Although the assumption of elliptical symmetry is quite common in multivariate analysis and widespread in a number of applications, the problem of testing the null hypothesis of ellipticity so far has not been addressed in a fully…

Generalized t-tests are constructed under weaker than normal conditions. In the first part of this paper we assume only the symmetry (around zero) of the error distribution (i). In the second part we assume that the error distribution is a…

New asymptotic approximations of the non-central $t$ distribution are given, a generalization of the Student's $t$ distribution. Using new integral representations, we give new asymptotic expansions for large values of the noncentrality…

This paper investigates weighted approximations for studentized $U$-statistics type processes, both with symmetric and antisymmetric kernels, only under the assumption that the distribution of the projection variate is in the domain of…

We develop some graph-based tests for spherical symmetry of a multivariate distribution using a method based on data augmentation. These tests are constructed using a new notion of signs and ranks that are computed along a path obtained by…

Testing symmetry of a probability distribution is a common question arising from applications in several fields. Particularly, in the study of observables used in the analysis of stock market index variations, the question of symmetry has…

We consider tests of hypotheses when the parameters are not identifiable under the null in semiparametric models, where regularity conditions for profile likelihood theory fail. Exponential average tests based on integrated profile…

In this paper, we propose optimal tests for circular reflective symmetry about a fixed median direction. The distributions against which optimality is achieved are the so-called k-sine-skewed distributions of Umbach and Jammalamadaka…