Related papers: On uniformly consistent tests
We consider the covering of a ball in certain normed spaces by its congruent subsets and show that if the finite number of sets is not greater than the dimensionality of the space, then the centre of the ball either belongs to the interior…
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…
Bayesian and frequentist criteria fundamentally differ, but often posterior and sampling distributions agree asymptotically (e.g., Gaussian with same covariance). For the corresponding single-draw experiment, we characterize the frequentist…
Building on ideas from Castillo and Nickl [Ann. Statist. 41 (2013) 1999-2028], a method is provided to study nonparametric Bayesian posterior convergence rates when "strong" measures of distances, such as the sup-norm, are considered. In…
Estimation of structure, such as in variable selection, graphical modelling or cluster analysis is notoriously difficult, especially for high-dimensional data. We introduce stability selection. It is based on subsampling in combination with…
It is well-known that density estimation on the unit interval is asymptotically equivalent to a Gaussian white noise experiment, provided the densities have H\"older smoothness larger than $1/2$ and are uniformly bounded away from zero. We…
Hypothesis testing results often rely on simple, yet important assumptions about the behaviour of the distribution of p-values under the null and the alternative. We examine tests for one dimensional parameters of interest that converge to…
Ratios of universal enumerable semimeasures corresponding to hypotheses are investigated as a solution for statistical composite hypotheses testing if an unbounded amount of computation time can be assumed. Influence testing for discrete…
Recent advances have demonstrated the possibility of solving the deconvolution problem without prior knowledge of the noise distribution. In this paper, we study the repeated measurements model, where information is derived from multiple…
After variable selection, standard inferential procedures for regression parameters may not be uniformly valid; there is no finite-sample size at which a standard test is guaranteed to approximately attain its nominal size. This problem is…
The classical Busemann-Petty problem asks whether smaller central hyperplane sections of origin-symmetric convex bodies necessarily imply smaller total volume. Zvavitch studied this question for arbitrary measures with continuous even…
We study the compatibility of measurements on finite-dimensional compact convex state space in the framework of general probabilistic theory. Our main emphasis is on formulation of necessary and sufficient conditions for two-outcome…
In this paper we consider the isoperimetric problem with double density in an Euclidean space, that is, we study the minimisation of the perimeter among subsets of $\mathbb{R}^n$ with fixed volume, where volume and perimeter are relative to…
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 show that for a convex solid set of positive random variables to be tight, or equivalently bounded in probability, it is necessary and sufficient that it is radially bounded, i.e. that every ray passing through one of its elements…
This is a report of a joint work with E. J\"arvenp\"a\"a, M. J\"arvenp\"a\"a, T. Rajala, S. Rogovin, and V. Suomala. In [3], we characterized uniformly porous sets in $s$-regular metric spaces in terms of regular sets by verifying that a…
In this paper we propose a Bayesian answer to testing problems when the hypotheses are not well separated. The idea of the method is to study the posterior distribution of a discrepancy measure between the parameter and the model we want to…
In observational studies of discrimination, the most common statistical approaches consider either the rate at which decisions are made (benchmark tests) or the success rate of those decisions (outcome tests). Both tests, however, have…
In this work, we revisit the problem of uniformity testing of discrete probability distributions. A fundamental problem in distribution testing, testing uniformity over a known domain has been addressed over a significant line of works, and…
The Standard Simplex Conjecture and the Plurality is Stablest Conjecture are two conjectures stating that certain partitions are optimal with respect to Gaussian and discrete noise stability respectively. These two conjectures are natural…