Asymptotically Optimal Procedures for Sequential Joint Detection and Estimation

TL;DR

This paper develops an asymptotically optimal sequential procedure for joint hypothesis testing and parameter estimation, minimizing sample use while controlling errors, suitable for high-dimensional data.

Contribution

It introduces a computationally efficient, asymptotically optimal stopping rule and a quasi-Newton method for parameter tuning under error constraints.

Findings

Procedure becomes optimal as error levels approach zero

Method is computationally cheap for high-dimensional data

Validated by numerical experiments

Abstract

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 average as few samples as possible and keeping the detection and estimation errors below predefined levels. Based on mild assumptions on the underlying model, we propose an asymptotically optimal procedure, i.e., a procedure that becomes optimal when the tolerated detection and estimation error levels tend to zero. The implementation of the resulting asymptotically optimal stopping rule is computationally cheap and, hence, applicable for high-dimensional data. We further propose a projected quasi-Newton method to optimally choose the coefficients that parameterize the instantaneous cost function such that the constraints are fulfilled with equality. The proposed theory is validated by numerical examples.