Related papers: Tests for circular symmetry of complex-valued rand…
This paper proposes a class of origin-smooth approximators of indicators underlying the sum-of-negative-part statistic for testing multiple inequalities. The need for simulation or bootstrap to obtain test critical values is thereby…
Continuous and strictly positive data that exhibit skewness and outliers frequently arise in many applied disciplines. Log-symmetric distributions provide a flexible framework for modeling such data. In this article, we develop new…
We engineer a new probabilistic Monte-Carlo algorithm for isomorphism testing. Most notably, as opposed to all other solvers, it implicitly exploits the presence of symmetries without explicitly computing them. We provide extensive…
We describe a generalization of the group testing problem termed symmetric group testing. Unlike in classical binary group testing, the roles played by the input symbols zero and one are "symmetric" while the outputs are drawn from a…
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…
We investigate the properties of a sequential Monte Carlo method where the particle weight that appears in the algorithm is estimated by a positive, unbiased estimator. We present broadly-applicable convergence results, including a central…
Consider the empirical spectral distribution of complex random $n\times n$ matrix whose entries are independent and identically distributed random variables with mean zero and variance $1/n$. In this paper, via applying potential theory in…
We develop an asymptotic theory for $L^2$ norms of sample mean vectors of high-dimensional data. An invariance principle for the $L^2$ norms is derived under conditions that involve a delicate interplay between the dimension $p$, the sample…
A method is presented to tackle the sign problem in the simulations of systems having indefinite or complex-valued measures. In general, this new approach is shown to yield statistical errors smaller than the crude Monte Carlo using…
By random complex zeroes we mean the zero set of a random entire function whose Taylor coefficients are independent complex-valued Gaussian variables, and the variance of the k-th coefficient is 1/k!. This zero set is distribution invariant…
This paper introduces a comprehensive framework for complex-valued probability measures and explores their novel applications in information theory and statistical analysis. We define a complex probability measure as a phase-modulated…
We are interested in testing general linear hypotheses in a high-dimensional multivariate linear regression model. The framework includes many well-studied problems such as two-sample tests for equality of population means, MANOVA and…
We explore the probability that a permutation sampled from the symmetric group of order n uniformly at random has cycles of lengths not exceeding r. Asymptotic formulas valid in specified regions for the ratio n/r are obtained using the…
The problem of testing for the parametric form of the conditional variance is considered in a fully nonparametric regression model. A test statistic based on a weighted $L_2$-distance between the empirical characteristic functions of…
This paper considers the problem of testing whether there exists a non-negative solution to a possibly under-determined system of linear equations with known coefficients. This hypothesis testing problem arises naturally in a number of…
A new method based on the rejection sampling for finding statistical tests is proposed. This method is conceptually intuitive, easy to implement, and applicable for arbitrary dimension. To illustrate its potential applicability, three…
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…
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…
In this article, we rigorously establish the consistency of generalized cross-validation as a parameter-choice rule for solving inverse problems. We prove that the index chosen by leave-one-out GCV achieves a non-asymptotic, order-optimal…
Background and objective. Circular statistics and Rayleigh tests are important tools for analyzing the occurrence of cyclic events. However, current methods fail in the presence of measurement bias, such as incomplete or otherwise…