Related papers: Asymptotics Related to a Binary Search Scheme
A recent article on generalised linear mixed model asymptotics, Jiang et al. (2022), derived the rates of convergence for the asymptotic variances of maximum likelihood estimators. If $m$ denotes the number of groups and $n$ is the average…
Large-scale multiple testing problems require the simultaneous assessment of many p-values. This paper compares several methods to assess the evidence in multiple binomial counts of p-values: the maximum of the binomial counts after…
In the asymptotic theory of quantum hypothesis testing, the minimal error probability of the first kind jumps sharply from zero to one when the error exponent of the second kind passes by the point of the relative entropy of the two states…
We consider a permutation method for testing whether observations given in their natural pairing exhibit an unusual level of similarity in situations where any two observations may be similar at some unknown baseline level. Under a null…
In this paper, we study three asymptotic regimes that can be applied to ranking and selection (R&S) problems with general sample distributions. These asymptotic regimes are constructed by sending particular problem parameters (probability…
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…
In this article, we propose a new method for the fundamental task of testing for dependence between two groups of variables. The response densities under the null hypothesis of independence and the alternative hypothesis of dependence are…
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…
In group testing, the task is to identify defective items by testing groups of them together using as few tests as possible. We consider the setting where each item is defective with a constant probability $\alpha$, independent of all other…
We consider the problem of detecting the true quantum state among $r$ possible ones, based of measurements performed on $n$ copies of a finite-dimensional quantum system. A special case is the problem of discriminating between $r$…
This paper is part of series on self-contained papers in which a large part, if not the full extent, of the asymptotic limit theory of summands of independent random variables is exposed. Each paper of the series may be taken as review…
The task of binary quantum hypothesis testing is to determine the state of a quantum system via measurements on it, given the side information that it is in one of two possible states, say $\rho$ and $\sigma$. This task is generally studied…
This is my dissertation. Its research object is a symmetric group of permutations acting on a finite set. The density of permutations with a given cycle structure pattern is explored when the group order tends to infinity. New and sharper…
Binary classification is a task that involves the classification of data into one of two distinct classes. It is widely utilized in various fields. However, conventional classifiers tend to make overconfident predictions for data that…
Given observations from a stationary time series, permutation tests allow one to construct exactly level $\alpha$ tests under the null hypothesis of an i.i.d. (or, more generally, exchangeable) distribution. On the other hand, when the null…
The problem of hypothesis testing is examined from both the historical and Bayesian points of view in the case that sampling is from an underlying joint probability distribution and the hypotheses tested for are those of independence and…
Causal inference in completely randomized treatment-control studies with binary outcomes is discussed from Fisherian, Neymanian and Bayesian perspectives, using the potential outcomes framework. A randomization-based justification of…
This paper studies the sample complexity of searching over multiple populations. We consider a large number of populations, each corresponding to either distribution P0 or P1. The goal of the search problem studied here is to find one…
The paper is focused on the problem of estimating the probability $p$ of individual contaminated sample, under group testing. The precision of the estimator is given by the probability of proportional closeness, a concept defined in the…
Assume that we have a random sample from an absolutely continuous distribution (univariate, or multivariate) with a known functional form and some unknown parameters. In this paper, we have studied several parametric tests based on…