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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 equivaria
Externí odkaz:
http://arxiv.org/abs/2412.14391
Autor:
Chen, Hantao, Wang, Cheng
This paper is concerned with Spearman's correlation matrices under large dimensional regime, in which the data dimension diverges to infinity proportionally with the sample size. We establish the central limit theorem for the linear spectral statisti
Externí odkaz:
http://arxiv.org/abs/2411.15861
We consider two hypothesis testing problems for low-rank and high-dimensional tensor signals, namely the tensor signal alignment and tensor signal matching problems. These problems are challenging due to the high dimension of tensors and lack of mean
Externí odkaz:
http://arxiv.org/abs/2411.01732
This paper is devoted to the study of the general linear hypothesis testing (GLHT) problem of multi-sample high-dimensional mean vectors. For the GLHT problem, we introduce a test statistic based on $L^2$-norm and random integration method, and deduc
Externí odkaz:
http://arxiv.org/abs/2410.14120
In this paper, for the problem of heteroskedastic general linear hypothesis testing (GLHT) in high-dimensional settings, we propose a random integration method based on the reference L2-norm to deal with such problems. The asymptotic properties of th
Externí odkaz:
http://arxiv.org/abs/2409.12066
This paper proposes procedures for testing the equality hypothesis and the proportionality hypothesis involving a large number of $q$ covariance matrices of dimension $p\times p$. Under a limiting scheme where $p$, $q$ and the sample sizes from the $
Externí odkaz:
http://arxiv.org/abs/2409.06296
Autor:
Kager, Wouter, Meester, Ronald
We investigate the asymptotic relation between likelihood ratios and p-values. We do that in a setting in which exact computations are possible: a coin-tossing context where the hypotheses of interest address the success probability of the coin. We o
Externí odkaz:
http://arxiv.org/abs/2408.12905
In the statistical literature, as well as in artificial intelligence and machine learning, measures of discrepancy between two probability distributions are largely used to develop measures of goodness-of-fit. We concentrate on quadratic distances, w
Externí odkaz:
http://arxiv.org/abs/2407.16374
Autor:
Guella, Jean Carlo
In this paper, we characterize several classes of continuous radial basis functions that can be employed to determine whether a interaction of a probability is zero or not. These functions encompass standard independence tests but also the Lancaster/
Externí odkaz:
http://arxiv.org/abs/2407.06854
In this article, we introduce the novel concept of the second maximum of a Gaussian random field on a Riemannian submanifold. This second maximum serves as a powerful tool for characterizing the distribution of the maximum. By utilizing an ad-hoc Kac
Externí odkaz:
http://arxiv.org/abs/2406.18397