Stability estimating in optimal sequential hypotheses testing

Gordienko, Evgueni I., Novikov, Andrey, and Zaitseva, Elena. "Stability estimating in optimal sequential hypotheses testing." Kybernetika 45.2 (2009): 331-344. <http://eudml.org/doc/37730>.

@article{Gordienko2009,
abstract = {We study the stability of the classical optimal sequential probability ratio test based on independent identically distributed observations $X_1,X_2,\dots $ when testing two simple hypotheses about their common density $f$: $f=f_0$ versus $f=f_1$. As a functional to be minimized, it is used a weighted sum of the average (under $f_0$) sample number and the two types error probabilities. We prove that the problem is reduced to stopping time optimization for a ratio process generated by $X_1,X_2,\dots $ with the density $f_0$. For $\tau _*$ being the corresponding optimal stopping time we consider a situation when this rule is applied for testing between $f_0$ and an alternative $\tilde\{f\}_1$, where $\tilde\{f\}_1$ is some approximation to $f_1$. An inequality is obtained which gives an upper bound for the expected cost excess, when $\tau _*$ is used instead of the rule $\tilde\{\tau \}_*$ optimal for the pair $(f_0,\tilde\{f\}_1)$. The inequality found also estimates the difference between the minimal expected costs for optimal tests corresponding to the pairs $(f_0,f_1)$ and $(f_0,\tilde\{f\}_1)$.},
author = {Gordienko, Evgueni I., Novikov, Andrey, Zaitseva, Elena},
journal = {Kybernetika},
keywords = {sequential hypotheses test; simple hypothesis; optimal stopping; sequential probability ratio test; likelihood ratio statistic; stability inequality; sequential hypotheses test; simple hypothesis; optimal stopping; sequential probability ratio test; likelihood ratio statistic; stability; inequality},
language = {eng},
number = {2},
pages = {331-344},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Stability estimating in optimal sequential hypotheses testing},
url = {http://eudml.org/doc/37730},
volume = {45},
year = {2009},
}

TY - JOUR
AU - Gordienko, Evgueni I.
AU - Novikov, Andrey
AU - Zaitseva, Elena
TI - Stability estimating in optimal sequential hypotheses testing
JO - Kybernetika
PY - 2009
PB - Institute of Information Theory and Automation AS CR
VL - 45
IS - 2
SP - 331
EP - 344
AB - We study the stability of the classical optimal sequential probability ratio test based on independent identically distributed observations $X_1,X_2,\dots $ when testing two simple hypotheses about their common density $f$: $f=f_0$ versus $f=f_1$. As a functional to be minimized, it is used a weighted sum of the average (under $f_0$) sample number and the two types error probabilities. We prove that the problem is reduced to stopping time optimization for a ratio process generated by $X_1,X_2,\dots $ with the density $f_0$. For $\tau _*$ being the corresponding optimal stopping time we consider a situation when this rule is applied for testing between $f_0$ and an alternative $\tilde{f}_1$, where $\tilde{f}_1$ is some approximation to $f_1$. An inequality is obtained which gives an upper bound for the expected cost excess, when $\tau _*$ is used instead of the rule $\tilde{\tau }_*$ optimal for the pair $(f_0,\tilde{f}_1)$. The inequality found also estimates the difference between the minimal expected costs for optimal tests corresponding to the pairs $(f_0,f_1)$ and $(f_0,\tilde{f}_1)$.
LA - eng
KW - sequential hypotheses test; simple hypothesis; optimal stopping; sequential probability ratio test; likelihood ratio statistic; stability inequality; sequential hypotheses test; simple hypothesis; optimal stopping; sequential probability ratio test; likelihood ratio statistic; stability; inequality
UR - http://eudml.org/doc/37730
ER -