Related papers: Optimal sequential tests yield log-optimal e-proce…
The problem of joint detection and lossless source coding is considered. We derive asymptotically optimal decision rules for deciding whether or not a sequence of observations has emerged from a desired information source, and to compress…
Adaptive designs have been proposed for clinical trials in which the nuisance parameters or alternative of interest are unknown or likely to be misspecified before the trial. Whereas most previous works on adaptive designs and mid-course…
Widely used methods and software for group sequential tests of a null hypothesis of no treatment difference that allow for early stopping of a clinical trial depend primarily on the fact that sequentially-computed test statistics have the…
We consider the problem of detection of sparse anomalies when monitoring a large number of data streams continuously in time. This problem is addressed using anytime-valid tests. In the context of a normal-means model and for a fixed…
We present adaptive sequential SAA (sample average approximation) algorithms to solve large-scale two-stage stochastic linear programs. The iterative algorithm framework we propose is organized into \emph{outer} and \emph{inner} iterations…
Asymptotic statistical theory for estimating functions is reviewed in a generality suitable for stochastic processes. Conditions concerning existence of a consistent estimator, uniqueness, rate of convergence, and the asymptotic…
A zero-error coding scheme of asymptotic rate $ \log_2 (1+\sqrt{5}) - 1 $ was recently described for a communication channel composed of parallel asynchronous lines satisfying the so-called no switch assumption. We prove that this is in…
We develop E-variables for testing whether two or more data streams come from the same source or not, and more generally, whether the difference between the sources is larger than some minimal effect size. These E-variables lead to exact,…
We consider sequential hypothesis testing between two quantum states using adaptive and non-adaptive strategies. In this setting, samples of an unknown state are requested sequentially and a decision to either continue or to accept one of…
We consider optimal control of a multi-class queue in the Halfin--Whitt regime, and revisit the notion of asymptotic optimality and the associated optimality gaps. The existing results in the literature for such systems provide…
The main purpose of this chapter is to present some theoretical aspects of parametric estimation of L\'evy processes based on high-frequency sampling, with a focus on infinite activity pure-jump models. Asymptotics for several classes of…
If multiway cluster-robust standard errors are used routinely in applied economics, surprisingly few theoretical results justify this practice. This paper aims to fill this gap. We first prove, under nearly the same conditions as with…
We consider sequential selection of an alternating subsequence from a sequence of independent, identically distributed, continuous random variables, and we determine the exact asymptotic behavior of an optimal sequentially selected…
This article discusses a new technique to automatically generate test cases for object oriented programs. At the state of the art, the problem of generating adequate sets of complete test cases has not been satisfactorily solved yet. There…
In this paper, we have established a general framework of multistage hypothesis tests which applies to arbitrarily many mutually exclusive and exhaustive composite hypotheses. Within the new framework, we have constructed specific…
A recurring debate in the philosophy of statistics concerns what, exactly, should count as a measure of evidence for or against a given hypothesis. P-values, likelihood ratios, and Bayes factors all have their defenders. In this paper we…
The population $\mathrm{KL}_{\inf}$ is a fundamental quantity that appears in lower bounds for (asymptotically) optimal regret of pure-exploration stochastic bandit algorithms, and optimal stopping time of sequential tests. Motivated by…
We investigate the asymptotic behavior of sample functions of stable processes when $t{\to}\infty$. We compare our results with the iterated logarithm law, results for the first hitting time and most visited sites problems.
Let $X_1,X_2,...$ be a discrete-time stochastic process with a distribution $P_\theta$, $\theta\in\Theta$, where $\Theta$ is an open subset of the real line. We consider the problem of testing a simple hypothesis $H_0:$ $\theta=\theta_0$…
We derive a necessary and sufficient condition for a sequence of quantum measurements to achieve the optimal performance in quantum hypothesis testing. Using an information-spectrum method, we discuss what quantum measurement we should…