Showing papers on "Sequential probability ratio test published in 1980"

A Test of the Parameter of the Exponential Distribution in the Type I Censoring Case

Abstract: Consider a life-testing experiment subject to Type I censoring, where m items are put on test at the outset and are not replaced on failure. Assume an exponential failure distribution F(t) = 1 – exp (– t/θ). A test of H 0: θ ≥ ξ versus H 1: θ < ξ based on the maximum likelihood estimator of θ is proposed. It is shown that early termination of the test resulting in either acceptance or rejection of H 0 is possible. Critical points are presented. The test is shown to compare favorably with a test presented by Epstein (1954) in terms of power and expected duration time. A comparison of the test with the un-truncated and truncated sequential probability ratio test is also made.

Curtailed and uniformly most powerful sequential tests

Abstract: The final decision of a fixed-sample likelihood ratio test is often determilned before the entire sample is taken. Such a test can be curtailed as soon as the final decision becomes obvious. The construction and properties of these curtailed tests are described. A particular class of such tests contains sequential tests which are uniformly most powerful. The asymptotic efficiency of this class is investigated. 1. Introduction. The Neyman-Pearson lemma shows that a fixed-sample likelihood ratio test has the property that no other test based on the same information can improve upon its error probabilities. The Wald-Wolfowitz theorem shows that, under certain conditions, a sequential probability ratio test may be better than a fixed-sample likelihood ratio test in the sense of having no worse error probabilities but smaller average sample size. However, this improvement is achieved at the cost of using more observations some of the time. Besides, a sequential probability ratio

Complete Classes for Sequential Tests of Hypotheses

Abstract: We consider problems of sequential testing when the loss function is the sum of a component due to an error in the terminal decision and a cost of observation component. In all cases we establish a characterization of a complete class or an essentially complete class. In order to obtain such results for testing a null hypothesis against an alternative hypothesis we establish complete class results for testing the closure of the null hypothesis against the closure of the alternative hypothesis. A complete class for testing closure of null against closure of alternative is an essentially complete class for testing null against alternative. Furthermore, a complete class for testing closure of null against closure of alternative is a complete class for testing null against alternative when the risks have certain continuity properties. Such continuity properties do hold in many cases. Three models are treated. The first is when the closure of the null space is compact and the cost of the first observation is positive. Under very unrestrictive conditions it is shown that the Bayes tests form a complete class. This result differs considerably from most fixed sample analogues that have been studied. The second model is when the closure of the null space is compact, the distributions are exponential family, and the cost of the first observation is zero. The third model is for the one dimensional exponential family case when the hypotheses are one sided.

Sequential Estimation of the Mean of a Multinormal Population

Abstract: This article is a multivariate generalization of the sequential sampling procedure developed by Robbins (1959) and extended by Starr (1966b) for estimating the mean of a normal population when the scale parameter is unknown. The exact distribution of the stopping time is derived for the sequential procedure, and a recursive method for computing the distribution of the stopping time is proposed that can be easily programmed for mechanical calculation. It is shown that the “risk efficiency” of the sequential procedure is a function of the dimension of the population.

Optimizing cervical specimen classifiers

Abstract: In an automated cervical cancer screening program, a prescreening machine could pass suspicious specimens to a cytotechnologist or cytopathologist while eliminating the normals from human consideration. This decision should be made at minimum cost consistent with acceptable false negative error rates. The sequential probability ratio test allows the designer to specify the probability of detection, select the false positive rate to minimize the overall cost of the test, and determine the expected cost of operating the system. The paper formulates that approach and presents specific examples based on actual cell classification experiments to illustrate the trade-off between operating cost and probability of detection.

A modification of the sequential probability ratio test for testing a normal mean

Abstract: Summary A modification of the sequential probability ratio test is proposed in which Wald's parallel boundaries are broken at some preassigned point of the sample number axis and Anderson's converging boundaries are used prior to that. Read's partial sequential probability ratio test can be considered as a special case of the proposed procedure. As far as ‘the maximum average sample number reducing property is concerned, the procedure is as good as Anderson's modified sequential probability ratio test.

Robust detection and estimation of soft failures in linear systems

Abstract: Algorithms for the robust detection and estimation of soft failures which have very modest computational requirements are presented. Soft failures are characterized by deviations in the statistical parameters of system inputs and measurement errors. The on-line detection scheme utilizes a single Kalman filter and requires the implementation of Wald Sequential Detectors (WSD). The algorithm consists of repeated application of the Sequential Probability Ratio Test (SPRT) to the filter innovations and use of the sequence of Sample Numbers (SN) for each SPRT termination for the detection of a failure. The proposed scheme for the estimation of a failed parameter consists of a bank of detectors and utilizes the properties of the Average Sample Number (ASN). The capabilities of the scheme, including its robustness for the isolation of single parameter failures, are illustrated via simulation results for a maneuvering target problem.

Sequential procedures in identification

Abstract: In this paper we study the problem of identifying a popula-tion with one of the two populations, with an aim to control both types of errors We assume that the populations are normal with unknown means, but with unit variance We have cited examples from anthropological studies where our formulation of the problem fits in quite nicely We observe that SPRT’s based on the maximal invariant may not terminate with probability one Simulation studies reported here show a substantial saving in the average number of samples compared to the best invariant fixed sample test

A Comparison of Adaptive Sequential, and Conventional Testing Strategies for Mastery Decisions.

Abstract: : Two procedures for making mastery decisions with variable length tests and a conventional mastery testing procedure were compared in Monte Carlo simulation. The simulation varied the characteristics of the item pool used for testing and the maximum test length allowed. The procedures were compared in terms of the mean test length needed to make a decision, the validity of the decisions made by each procedure, and the types of classification errors made by each procedure. Both of the variable test length procedures were found to result in important reductions in mean test length from the conventional test length. The Sequential Probability Ratio Test (SPRT) procedure resulted in greater test length reductions, on the average, than the Adaptive Mastery Testing (AMT) procedure. However, the AMT procedure resulted both in more valid mastery decisions and in more balanced error rates than the SPRT procedure under all conditions. In addition, the AMT procedure produced the best combination of test length and validity. (Author)

A simple sequential criterion for testing a normal mean with unknown variance

Abstract: Simply fully sequential tests of the null hypothesis, μ=μoversus an alternative either of the form , are proposed for a normal population with mean y and unknown variance. Both tests are shown to terminate finitely with prob-ability one; other properties of the tests are discussed. Simu-lation is used to estimate the true error frequencies and average sample sizes of the tests and to compare the proposed one-sided.test with Bartlett' (1946) test.

A generalization of anderson's modified sequential probability ratio test

Abstract: A generalization of Anderson's sequential probability ratio test procedure is proposed in which the continuation region is bounded by a pair of converging lines up to a certain stage of the experiment and later by another pair of converging lines until the procedure is truncated at a predetermined stage of the experiment. The OC and the ASN functions have been derived. For certain parameter values the proposed procedure attains lower average sample numbers than that attainable by any other known procedure.

Sequential analysis applied to testing the mean of a mormal population with known coefficient of variation

Abstract: Given a normal population with mean y and known coefficient of variation the hypothesis H0:μ=μ0 is tested against H1:μ=μ1 using the sequential probability ratio test. The maximum of the expected sample number is shown to occur when μ is approxi¬mately equal to the harmonic mean of μ0 and μ1 and it is shown that this maximum value depends on μ0 and μ1, only through and it is found that the above test might be used to test H0:μ≦μ0 yntheir ratio. The operating characteristic function is investigated and it is found that the above test might be used to test against H1:μ≧μ1.

An examination of the performance of two acceptance decision rules for curtailed wald sequential sampling plans.

Abstract: : This paper examines the implications on acceptance sampling decisions when the Wald Sequential Probability Ratio (SPR) Sampling process is curtailed. Two procedures are proposed to determine the stopping rules. The first procedure uses the scope of the least-square fitted line compared with the slope of the boundary lines of a Wald SPR Sampling Plan. The second procedure uses the relative position of the last observation between the rejection acceptance lines to determine the stopping rules. Computer programs are used to simulate the sampling process, proving estimates of operating characteristic points. (Author)

A modification of the partial sequential probability ratio test

Abstract: For the problem of discriminating between two simple hypoth¬eses concerning a Koopman - Darmois parameter, a modification of the partial sequential probability ratio test is proposed where instead of drawing only one fixed sample, two fixed samples are drawn and then Wald's SPRT is started The OC and the ASN func¬tions are derived Numerical comparisons are made with Wald's and Read's procedures for testing the normal mean with known variance For some parameter values, the test procedure has a lower ASN than that of Read's procedure