Related papers: Sequential Multiple Testing: A Second-Order Asympt…
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…
We treat a random number generation from an i.i.d. probability distribution of $P$ to that of $Q$. When $Q$ or $P$ is a uniform distribution, the problems have been well-known as the uniform random number generation and the resolvability…
Financial statement auditing is conducted under a risk-based evidence approach to obtain reasonable assurance. In practice, auditors often perform additional sampling or related procedures when an initial sample does not provide a…
We provide an asymptotic expansion of the maximal mean squared error (MSE) of the sample median to be attained on shrinking gross error neighborhoods about an ideal central distribution. More specifically, this expansion comes in powers of…
It has been recently shown that e-processes are sufficient for sequential testing in the following sense: every level-$\alpha$ sequential test can be obtained by thresholding an e-process at $1/\alpha$. However, in the above result, neither…
We study the mismatched successive refinement problem where one uses Gaussian codebooks to compress an arbitrary memoryless source with successive minimum Euclidean distance encoding under the quadratic distortion measure. Specifically, we…
We address the problem of searching for a change point in an anomalous process among a finite set of M processes. Specifically, we address a composite hypothesis model in which each process generates measurements following a common…
This paper studies the problem of high-dimensional multiple testing and sparse recovery from the perspective of sequential analysis. In this setting, the probability of error is a function of the dimension of the problem. A simple…
The design of multiple experiments is commonly undertaken via suboptimal strategies, such as batch (open-loop) design that omits feedback or greedy (myopic) design that does not account for future effects. This paper introduces new…
In this paper, we study sequential testing problems with \emph{overlapping} hypotheses. We first focus on the simple problem of assessing if the mean $\mu$ of a Gaussian distribution is smaller or larger than a fixed $\epsilon>0$; if…
Multi-stream sequential change detection involves simultaneously monitoring many streams of data and trying to detect when their distributions change, if at all. Here, we theoretically study multiple testing issues that arise from detecting…
We investigate the problem of jointly testing two hypotheses and estimating a random parameter based on data that is observed sequentially by sensors in a distributed network. In particular, we assume the data to be drawn from a Gaussian…
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…
There has been remarkable progress over the past decade in establishing finite-sample, non-asymptotic bounds on recovering unknown system parameters from observed system behavior. Surprisingly, however, we show that the current…
We consider the problem of simultaneous detection and estimation under a sequential framework. In particular we are interested in sequential tests that distinguish between the null and the alternative hypothesis and every time the decision…
This paper considers the problem of channel coding with a given (possibly suboptimal) maximum-metric decoding rule. A cost-constrained random-coding ensemble with multiple auxiliary costs is introduced, and is shown to achieve error…
A parameter estimation problem is considered, in which dispersed sensors transmit to the statistician partial information regarding their observations. The sensors observe the paths of continuous semimartingales, whose drifts are linear…
This work investigates the sequential hypothesis testing problem with online sensor selection and sensor usage constraints. That is, in a sensor network, the fusion center sequentially acquires samples by selecting one "most informative"…
Under mild Markov assumptions, sufficient conditions for strict minimax optimality of sequential tests for multiple hypotheses under distributional uncertainty are derived. First, the design of optimal sequential tests for simple hypotheses…
We consider a quantum system that is being continuously monitored, giving rise to a measurement signal. From such a stream of data, information needs to be inferred about the underlying system's dynamics. Here we focus on hypothesis testing…