Related papers: Testing convexity of a discrete distribution
This paper concerns a method of testing equality of distribution of random convex compact sets and the way how to use the test to distinguish between two realisations of general random sets. The family of metrics on the space of…
This paper develops a smooth test of goodness-of-fit for elliptical distributions. The test is adaptively omnibus, invariant to affine-linear transformations and has a convenient expression that can be broken into components. These…
We present a novel approach to estimating discrete distributions with (potentially) infinite support in the total variation metric. In a departure from the established paradigm, we make no structural assumptions whatsoever on the sampling…
In this paper we shall consider some famous means such as arithmetic, harmonic, geometric, root square mean, etc. Considering the difference of these means, we can establish. some inequalities among them. Interestingly, the difference of…
In this paper, we further develop the approach, originating in [14 (arXiv:1311.6765),20 (arXiv:1604.02576)], to "computation-friendly" hypothesis testing and statistical estimation via Convex Programming. Specifically, we focus on…
In this article we study the problem of quantifying the uncertainty in an experiment with a technical system. We propose new density estimates which combine observed data of the technical system and simulated data from an (imperfect)…
We investigate a data-driven approach to constructing uncertainty sets for robust optimization problems, where the uncertain problem parameters are modeled as random variables whose joint probability distribution is not known. Relying only…
We consider the problem of sequentially testing a simple null hypothesis versus a composite alternative hypothesis that consists of a finite set of densities. We study sequential tests that are based on thresholding of mixture-based…
Assessing the validity of a real-world system with respect to given quality criteria is a common yet costly task in industrial applications due to the vast number of required real-world tests. Validating such systems by means of simulation…
Classical two-sample permutation tests for equality of distributions have exact size in finite samples, but they fail to control size for testing equality of parameters that summarize each distribution. This paper proposes permutation tests…
We introduce estimation and test procedures through divergence optimization for discrete or continuous parametric models. This approach is based on a new dual representation for divergences. We treat point estimation and tests for simple…
We consider the estimation of the total number $N$ of species based on the abundances of species that have been observed. We adopt a non parametric approach where the true abundance distribution $p$ is only supposed to be convex. From this…
Recently Liu and Wang derived the likelihood ratio test (LRT) statistic and its asymptotic distribution for testing equality of two multinomial distributions vs. the alternative that the second distribution is larger in terms of increasing…
Given a compactly supported probability measure on a Riemannian manifold, we study the asymptotic speed at which it can be approximated (in Wasserstein distance of any exponent p) by finitely supported measure. This question has been…
We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…
This paper develops a unified framework for asymptotically minimax robust hypothesis testing under distributional uncertainty, applicable to both Bayesian and Neyman--Pearson formulations (Type-I and Type-II). Uncertainty classes based on…
We consider spline estimates which preserve prescribed piecewise convex properties of the unknown function. A robust version of the penalized likelihood is given and shown to correspond to a variable halfwidth kernel smoother where the…
We consider a two-component mixture model with one known component. We develop methods for estimating the mixing proportion and the unknown distribution nonparametrically, given i.i.d.~data from the mixture model, using ideas from shape…
We investigate the high-probability estimation of discrete distributions from an \iid sample under $\chi^2$-divergence loss. Although the minimax risk in expectation is well understood, its high-probability counterpart remains largely…
We study local asymptotic normality of M-estimates of convex minimization in an infinite dimensional parameter space. The objective function of M-estimates is not necessary differentiable and is possibly subject to convex constraints. In…