Related papers: Testing the Isotropic Cauchy Hypothesis

The results of a series of theoretical studies are reported, examining the convergence rate for different approximate representations of $\alpha$-stable distributions. Although they play a key role in modelling random processes with jumps…

We study a variant of the simple hypothesis testing problem where observed samples do not necessarily come from either of the specified distributions, but rather from a close variant of them. In this setting, we require a test that is…

When data analysts train a classifier and check if its accuracy is significantly different from chance, they are implicitly performing a two-sample test. We investigate the statistical properties of this flexible approach in the…

For an isotropic convex body $K\subset\mathbb{R}^n$ we consider the isotropic constant $L_{K_N}$ of the symmetric random polytope $K_N$ generated by $N$ independent random points which are distributed according to the cone probability…

We consider $n\times n$ random matrices $M_{n}=\sum_{\alpha =1}^{m}{\tau _{\alpha }}\mathbf{y}_{\alpha }\otimes \mathbf{y}_{\alpha }$, where $\tau _{\alpha }\in \mathbb{R}$, $\{\mathbf{y}_{\alpha }\}_{\alpha =1}^{m}$ are i.i.d. isotropic…

We consider the problem of hypotheses testing with the basic simple hypothesis: observed sequence of points corresponds to stationary Poisson process with known intensity against a composite one-sided parametric alternative that this is a…

We study the distributions of the LASSO, SCAD, and thresholding estimators, in finite samples and in the large-sample limit. The asymptotic distributions are derived for both the case where the estimators are tuned to perform consistent…

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…

Motivated by the problem of testing for the existence of a signal of known parametric structure and unknown ``location'' (as explained below) against a noisy background, we obtain for the maximum of a centered, smooth random field an…

We establish a rigorous asymptotic theory for the joint estimation of roughness and scale parameters in two-dimensional Gaussian random fields with power-law generalized covariances \cite{Matheron1973, Stein1999, Yaglom1987}. Our main…

In this paper the elicitation of probabilities from human experts is considered as a measurement process, which may be disturbed by random 'measurement noise'. Using Bayesian concepts a second order probability distribution is derived…

The exact expression for the probability density $p_{_N}(x)$ for sums of a finite number $N$ of random independent terms is obtained. It is shown that the very tail of $p_{_N}(x)$ has a Gaussian form if and only if all the random terms are…

In this note, we review some of the recent developments in the well-posedness theory of nonlinear dispersive partial differential equations with random initial data.

In the probability theory limit distributions (or probability measures) are often characterized by some convolution equations (factorization properties) rather than by Fourier transforms (the characteristic functionals). In fact, usually…

We propose two robust methods for testing hypotheses on unknown parameters of predictive regression models under heterogeneous and persistent volatility as well as endogenous, persistent and/or fat-tailed regressors and errors. The proposed…

In this paper a robust version of the classical Wald test statistics for linear hypothesis in the logistic regression model is introduced and its properties are explored. We study the problem under the assumption of random covariates…

Motivated by real-world machine learning applications, we analyze approximations to the non-asymptotic fundamental limits of statistical classification. In the binary version of this problem, given two training sequences generated according…

In the Bayes paradigm and for a given loss function, we propose the construction of a new type of posterior distributions, that extends the classical Bayes one, for estimating the law of an $n$-sample. The loss functions we have in mind are…

Hypothesis testing in contingency tables is usually based on asymptotic results, thereby restricting its proper use to large samples. To study these tests in small samples, we consider the likelihood ratio test and define an accurate index,…

An important aspect of multiple hypothesis testing is controlling the significance level, or the level of Type I error. When the test statistics are not independent it can be particularly challenging to deal with this problem, without…