Second-Order Asymptotics of Sequential Hypothesis Testing

01/14/2020
by   Yonglong Li, et al.
0

We consider the classical sequential binary hypothesis testing problem in which there are two hypotheses governed respectively by distributions P 0 and P 1 and we would like to decide which hypothesis is true using a sequential test. It is known from the work of Wald and Wolfowitz that as the expectation of the length of the test grows, the optimal type-I and type-II error exponents approach the relative entropies D(P _1 P_0 ) and D(P_0 P_1). We refine this result by considering the optimal backoff from the corner point of the achievable exponent region (D(P _1 P_0 ), D(P_0 P_1 )) under two different constraints on the length of the test (or the sample size). First, we consider a probabilistic constraint in which the probability that the length of test exceeds a prescribed integer n is less than a certain threshold 0 <ε < 1. Second, the expectation of the sample size is bounded by n. In both cases, and under mild conditions, the backoff, also coined second-order asymptotics, is characterized precisely. Examples are provided to illustrate our results.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
06/02/2021

Asymptotics of Sequential Composite Hypothesis Testing under Probabilistic Constraints

We consider the sequential composite binary hypothesis testing problem i...
research
10/23/2022

Achievable Error Exponents for Almost Fixed-Length Hypothesis Testing and Classification

We revisit multiple hypothesis testing and propose a two-phase test, whe...
research
05/11/2022

Second-Order Asymptotics of Hoeffding-Like Hypothesis Tests

We consider a binary statistical hypothesis testing problem, where n ind...
research
10/08/2021

Optimal Group-Sequential Tests with Groups of Random Size

We consider sequential hypothesis testing based on observations which ar...
research
11/30/2020

On Error Exponents of Almost-Fixed-Length Channel Codes and Hypothesis Tests

We examine a new class of channel coding strategies, and hypothesis test...
research
10/31/2022

Cost-aware Generalized α-investing for Multiple Hypothesis Testing

We consider the problem of sequential multiple hypothesis testing with n...
research
12/03/2019

Sequential Classification with Empirically Observed Statistics

Motivated by real-world machine learning applications, we consider a sta...

Please sign up or login with your details

Forgot password? Click here to reset