Related papers: Optimal tests for circular reflective symmetry abo…
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…
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…
Motivated by the central role played by rotationally symmetric distributions in directional statistics, we consider the problem of testing rotational symmetry on the hypersphere. We adopt a semiparametric approach and tackle problems where…
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…
Testing uniformity on the $p$-dimensional unit sphere is arguably the most fundamental problem in directional statistics. In this paper, we consider this problem in the framework of axial data, that is, under the assumption that the $n$…
We propose tests for the null hypothesis that the law of a complex-valued random vector is circularly symmetric. The test criteria are formulated as $L^2$-type criteria based on empirical characteristic functions, and they are convenient…
In this paper, some recent and classical tests of symmetry are modified for the case of an unknown center. The unknown center is estimated with its $\alpha$-trimmed mean estimator. The asymptotic behavior of the new tests is explored. The…
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 objective of this paper is to provide, for the problem of univariate symmetry (with respect to specified or unspecified location), a concept of optimality, and to construct tests achieving such optimality. This requires embedding…
We consider the problem of testing whether a multivariate distribution is axially symmetric about some unknown direction. Under a simple-spectrum assumption on the covariance matrix, any symmetry axis must coincide with an eigenvector of…
We propose confidence regions for the parameters of incomplete models with exact coverage of the true parameter in finite samples. Our confidence region inverts a test, which generalizes Monte Carlo tests to incomplete models. The test…
In this paper optimal experimental designs for inverse quadratic regression models are determined. We consider two different parameterizations of the model and investigate local optimal designs with respect to the $c$-, $D$- and…
Monte Carlo approximations for random linear elliptic PDE constrained optimization problems are studied. We use empirical process theory to obtain best possible mean convergence rates $O(n^{-\frac{1}{2}})$ for optimal values and solutions,…
Testing procedures for assessing a parametric regression model with circular response and $\mathbb{R}^d$-valued covariate are proposed and analyzed in this work both for independent and for spatially correlated data. The test statistics are…
In view of the great performance of circumcentered isometry methods for solving the best approximation problem, in this work we further investigate the locally proper circumcenter mapping and circumcentered method. Various examples of…
We consider the problem of testing, on the basis of a $p$-variate Gaussian random sample, the null hypothesis ${\cal H}_0: {\pmb \theta}_1= {\pmb \theta}_1^0$ against the alternative ${\cal H}_1: {\pmb \theta}_1 \neq {\pmb \theta}_1^0$,…
Linear regression models are among the models most used in practice, although the practitioners are often not sure whether their assumed linear regression model is at least approximately true. In such situations, only designs for which the…
In many applications common in testing for convergence the number of cross-sectional units is large and the number of time periods are few. In these situations asymptotic tests based on an omnibus null hypothesis are characterised by a…
This paper provides parametric and rank-based optimal tests for eigenvectors and eigenvalues of covariance or scatter matrices in elliptical families. The parametric tests extend the Gaussian likelihood ratio tests of Anderson (1963) and…
We propose a class of rank-based procedures for testing that the shape matrix $\mathbf{V}$ of an elliptical distribution (with unspecified center of symmetry, scale and radial density) has some fixed value ${\mathbf{V}}_0$; this includes,…