Related papers: On Optimality of Stepdown and Stepup Multiple Test…
We revisit the outlier hypothesis testing framework of Li \emph{et al.} (TIT 2014) and derive fundamental limits for the optimal test. In outlier hypothesis testing, one is given multiple observed sequences, where most sequences are…
One class of statistical hypothesis testing procedures is the indisputable equivalence tests, whose main objective is to establish practical equivalence rather than the usual statistical significant difference. These hypothesis tests are…
This paper studies the problem of testing whether a function is monotone from a nonparametric Bayesian perspective. Two new families of tests are constructed. The first uses constrained smoothing splines, together with a hierarchical…
Modern statistical analyses often involve testing large numbers of hypotheses. In many situations, these hypotheses may have an underlying tree structure that not only helps determine the order that tests should be conducted but also…
In existing simulation proof techniques, a single step in a lower-level specification may be simulated by an extended execution fragment in a higher-level one. As a result, it is cumbersome to mechanize these techniques using general…
In this paper, we study the problem of determining $k$ anomalous random variables that have different probability distributions from the rest $(n-k)$ random variables. Instead of sampling each individual random variable separately as in the…
In the realm of robust optimization the k-adaptability approach is one promising method to derive approximate solutions for two-stage robust optimization problems. Instead of allowing all possible second-stage decisions, the k-adaptability…
The problem of monotonicity testing over the hypergrid and its special case, the hypercube, is a classic, well-studied, yet unsolved question in property testing. We are given query access to $f:[k]^n \mapsto \R$ (for some ordered range…
The most popular multiple testing procedures are stepwise procedures based on $P$-values for individual test statistics. Included among these are the false discovery rate (FDR) controlling procedures of Benjamini--Hochberg [J. Roy. Statist.…
We first review existing sequential methods for estimating a binomial proportion. Afterward, we propose a new family of group sequential sampling schemes for estimating a binomial proportion with prescribed margin of error and confidence…
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…
In this paper, we deal with sequential testing of multiple hypotheses. In the general scheme of construction of optimal tests based on the backward induction, we propose a modification which provides a simplified (generally speaking,…
Many multiple testing procedures make use of the p-values from the individual pairs of hypothesis tests, and are valid if the p-value statistics are independent and uniformly distributed under the null hypotheses. However, it has recently…
We analyze an optimal stopping problem with random maturity under a nonlinear expectation with respect to a weakly compact set of mutually singular probabilities $\mathcal{P}$. The maturity is specified as the hitting time to level $0$ of…
A central problem in Binary Hypothesis Testing (BHT) is to determine the optimal tradeoff between the Type I error (referred to as false alarm) and Type II (referred to as miss) error. In this context, the exponential rate of convergence of…
Nonsmooth nonconvex optimization problems involving the $\ell^p$ quasi-norm, $p \in (0, 1]$, of a linear map are considered. A monotonically convergent scheme for a regularized version of the original problem is developed and necessary…
We formulate nonparametric and semiparametric hypothesis testing of multivariate stationary linear time series in a unified fashion and propose new test statistics based on estimators of the spectral density matrix. The limiting…
Given a fixed-sample-size test that controls the error probabilities under two specific, but arbitrary, distributions, a 3-stage and two 4-stage tests are proposed and analyzed. For each of them, a novel, concrete, non-asymptotic,…
Machine learning applications frequently come with multiple diverse objectives and constraints that can change over time. Accordingly, trained models can be tuned with sets of hyper-parameters that affect their predictive behavior (e.g.,…
Symmetry plays a crucial role in quantum physics, dictating the behavior and dynamics of physical systems. In this paper, we develop a hypothesis-testing framework for quantum dynamics symmetry using a limited number of queries to the…