Sequential probability ratio test

About: Sequential probability ratio test is a research topic. Over the lifetime, 1248 publications have been published within this topic receiving 22355 citations.

On the Admissibility or Inadmissibility of Fixed Sample Size Tests in a Sequential Setting

Abstract: Questions pertaining to the admissibility of fixed sample size tests of hypotheses, when sequential tests are available, are considered. For the normal case with unknown mean, suppose the risk function is a linear combination of probability of error and expected sample size. Then any fixed sample size test, with sample size $n \geqslant 2$, is inadmissible. On the other hand, suppose the risk function consists of the pair of components, probability of error and expected sample size. Then any optimal fixed sample size test for the one sided hypothesis is admissible. When the variance of the normal distribution is unknown, $t$-tests are studied. For one-sided hypotheses and componentwise risk functions the fixed sample size $t$-test is inadmissible if and only if the absolute value of the critical value of the test is greater than or equal to one. This implies that for the most commonly used sizes, the fixed sample size $t$-test is inadmissible. Other loss functions are discussed. Also an example for a normal mean problem is given where a nonmonotone test cannot be improved on by a monotone test when the risk is componentwise.

Fault detection using sequential probability ratio test

Abstract: This paper describes a method for detecting power system faults based on the sequential probability ratio test (SPRT) and Kalman filter. The SPRT is the optimal statistical test that makes the correct decision in the shortest time among all tests that are subject to the same level of decision errors. Simulation results are provided to show the superiority of the proposed method.

Performance analysis of Wald's SPRT with independent but non-stationary log-likelihood ratios

Abstract: The characteristics and behavior of Wald's sequential probability ratio test are revealed by two important functions — operating characteristic (OC) and average sample number (ASN). These two functions have been studied extensively under the assumption of independent and identically distributed (i.i.d.) log-likelihood ratios, which is too stringent for many applications. This paper relaxes the requirement of identical distribution. Two inductive equations governing the OC and ASN are developed. Unfortunately, they have non-unique solutions in the general case. They do have unique solutions in two special cases: (a) the log-likelihood ratios converge in distributions and (b) the log-likelihood ratios have periodic distributions. Numerical solutions for these two special cases are obtained. They are compared with the results of Monte Carlo simulations because existing methods for this problem setting are lacking.

Time-Sequential Sampling: A New Use of the Sequential Probability Ratio Test for Pest Management Decisions

Abstract: Amethod was developed to use the sequential probability ratio test of Wald (sequential sampling) in a time-oriented sense rather than in a spatial sense. The method allows a grower or scout to decide if a population is of an endemic or outbreak type on the basis of mathematical dispersion and differential growth rates of the types. Formulas and calculations are presented for data from negative-binomial, Poisson, and binomial distributions. An example of time-sequential sampling is presented for immigrant green cloverworm adults on soybean. The use and position of time-sequential sampling in the green cloverworm pest management subsystem is indicated.