Related papers: Efficient three-stage $t$-tests
We study Probabilistic Group Testing of a set of N items each of which is defective with probability p. We focus on the double limit of small defect probability, p<<1, and large number of variables, N>>1, taking either p->0 after…
It is more important to estimate the rate of convergence to a stationary distribution rather than only to prove the existence one in many applied problems of reliability and queuing theory. This can be done via standard methods, but only…
Adaptive experiments are becoming increasingly popular in real-world applications for effectively maximizing in-sample welfare and efficiency by data-driven sampling. Despite their growing prevalence, however, the statistical foundations…
In the group testing problem the aim is to identify a small set of $k\sim n^\theta$ infected individuals out of a population size $n$, $0<\theta<1$. We avail ourselves of a test procedure capable of testing groups of individuals, with the…
We propose a new class of semiparametric exponential family graphical models for the analysis of high dimensional mixed data. Different from the existing mixed graphical models, we allow the nodewise conditional distributions to be…
We give a general unified method that can be used for $L_1$ {\em closeness testing} of a wide range of univariate structured distribution families. More specifically, we design a sample optimal and computationally efficient algorithm for…
We give a hybrid two stage design which can be useful to estimate the reliability of a parallel-series and/or by duality a series-parallel system, when the component reliabilities are unknown as well as the total numbers of units allowed to…
After a brief review of recent advances in sequential analysis involving sequential generalized likelihood ratio tests, we discuss their use in psychometric testing and extend the asymptotic optimality theory of these sequential tests to…
We consider the problem where an active Decision-Maker (DM) is tasked to identify the true hypothesis using as few samples as possible while maintaining accuracy. The DM collects samples according to its determined actions and knows the…
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…
In this paper, we consider sequential testing over a single-sensor, a single-decision center setup. At each time instant $t$, the sensor gets $k$ samples $(k>0)$ and describes the observed sequence until time $t$ to the decision center over…
This paper investigates improved testing inferences under a general multivariate elliptical regression model. The model is very flexible in terms of the specification of the mean vector and the dispersion matrix, and of the choice of the…
Analysis of low-degree polynomial algorithms is a powerful, newly-popular method for predicting computational thresholds in hypothesis testing problems. One limitation of current techniques for this analysis is their restriction to…
This paper studies a two-stage model of experimentation, where the researcher first samples representative units from an eligible pool, then assigns each sampled unit to treatment or control. To implement balanced sampling and assignment,…
For a set of dependent random variables, without stationary or the strong mixing assumptions, we derive the asymptotic independence between their sums and maxima. Then we apply this result to high-dimensional testing problems, where we…
We revisit outlier hypothesis testing, propose exponentially consistent low complexity fixed-length and sequential tests and show that our tests achieve better tradeoff between detection performance and computational complexity than…
The problem of joint sequential detection and isolation is considered in the context of multiple, not necessarily independent, data streams. A multiple testing framework is proposed, where each hypothesis corresponds to a different subset…
We treat quantum counterparts of testing problems whose optimal tests are given by chi-square, t and F tests. These quantum counterparts are formulated as quantum hypothesis testing problems concerning quantum Gaussian states families, and…
The Barzilai-Borwein (BB) steplengths play great roles in practical gradient methods for solving unconstrained optimization problems. Motivated by the observation that the two well-known BB steplengths correspond to the ordinary and the…
Many scientific applications involve testing theories that are only partially specified. This task often amounts to testing the goodness-of-fit of a candidate distribution while allowing for reasonable deviations from it. The tolerant…