Related papers: Second-Order Asymptotically Optimal Statistical Cl…
This paper is concerned with estimating the intersection point of two densities, given a sample of both of the densities. This problem arises in classification theory. The main results provide lower bounds for the probability of the…
Given samples from two non-negative random variables, we propose a family of tests for the null hypothesis that one random variable stochastically dominates the other at the second order. Test statistics are obtained as functionals of the…
We consider the \mnk{classical} problem of a controller activating (or sampling) sequentially from a finite number of $N \geq 2$ populations, specified by unknown distributions. Over some time horizon, at each time $n = 1, 2, \ldots$, the…
Suppose that we have two training sequences generated by parametrized distributions $P_{\theta^*}$ and $P_{\xi^*}$, where $\theta^*$ and $\xi^*$ are unknown true parameters. Given training sequences, we study the problem of classifying…
We investigate the nonparametric, composite hypothesis testing problem for arbitrary unknown distributions in the asymptotic regime where both the sample size and the number of hypotheses grow exponentially large. Such asymptotic analysis…
We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…
Second order asymptotics of fixed-length source coding and intrinsic randomness is discussed with a constant error constraint. There was a difference between optimal rates of fixed-length source coding and intrinsic randomness, which never…
Hierarchical statistical models are widely employed in information science and data engineering. The models consist of two types of variables: observable variables that represent the given data and latent variables for the unobservable…
Two types of errors can occur when discriminating pairs of quantum states. Asymmetric state discrimination involves minimizing the probability of one type of error, subject to a constraint on the other. We give explicit expressions bounding…
In group sequential designs, where several data looks are conducted for early stopping, we generally assume the vector of test statistics from the sequential analyses follows (at least approximately or asymptotially) a multivariate normal…
We derive the local and central limit theorems for the Stirling numbers of the second kind by elementary means, obtaining as corollaries effective asymptotic estimates for the Bell numbers and for the moments of the distribution. We also…
We consider nonparametric sequential hypothesis testing problem when the distribution under the null hypothesis is fully known but the alternate hypothesis corresponds to some other unknown distribution with some loose constraints. We…
The problem of testing two simple hypotheses in a general probability space is considered. For a fixed type-I error probability, the best exponential decay rate of the type-II error probability is investigated. In regular asymptotic cases…
We provide non-asymptotic bounds for first and higher order inclusion probabilities of the rejective sampling model with various size parameters. Further we derive bounds in the semi-definite ordering for matrices that collect (conditional)…
The problem of simultaneously testing the marginal distributions of sequentially monitored, independent data streams is considered. The decisions for the various testing problems can be made at different times, using data from all streams,…
We revisit resampling procedures for error estimation in binary classification in terms of U-statistics. In particular, we exploit the fact that the error rate estimator involving all learning-testing splits is a U-statistic. Thus, it has…
Specimens are collected from $N$ different sources. Each specimen has probability $p$ of being contaminated, independently of the other specimens. We assume group testing is applicable, namely one can take small portions from several…
The asymptotically optimal hypothesis testing problem with the general sources as the null and alternative hypotheses is studied under exponential-type error constraints on the first kind of error probability. Our fundamental philosophy in…
We investigate the problem of jointly testing multiple hypotheses and estimating a random parameter of the underlying distribution in a sequential setup. The aim is to jointly infer the true hypothesis and the true parameter while using on…
We study learning of probability distributions characterized by an unknown symmetry direction. Based on an entropic performance measure and the variational method of statistical mechanics we develop exact upper and lower bounds on the…