Showing papers on "Sequential probability ratio test published in 1968"

Sequential Analysis, Direct Method

Abstract: This paper describes from first principles the direct calculation of the operating characteristic function, O.C., the probability of accepting the hypothesis θ = θ0, and the average sample size, A.S.N., required to terminate the test, for any truncated sequential test once the acceptance, rejection, and the continuation regions are specified at each stage. What is needed is to regard a sequential test as a step by step random walk, which is a Markov chain. The method is contrasted with Wald's and two examples are included.

Detection of Changes in the Characteristics of a Gauss-Markov Process

Abstract: By an extension to the theory of sequential detection with dependent measurements, it is possible to develop a sequential probability ratio test (SPRT) to detect changes in regime in a Gauss-Markov process rather than detecting which of the two regimes exists. It is shown how a posterior form of this extended SPRT may be simplified to reduce computational complexity. The simplified SPRT's are in fact modifications of the original SPRT detecting the regime and not the change. The tests are applied to the problem of fault detection in a gyro navigational system; the results of a detailed computer simulation are given.

Sequential Testing of Sample Size

Abstract: A sample of unknown size n is obtained from a known population. The order statistics are then examined sequentially for the purpose of drawing inferences about n. A procedure for testing the unknown sample size n is given and its exact properties are obtained. This procedure provides a basis for examining some popular conjectures and approximations in sequential analysis. In particular two suggested approximations to the average sample number of a sequential probability ratio test are discussed.

A distribution-free sequential probability-ratio test for multiple-resolution-element radars (Corresp.)

Abstract: A distribution-free procedure applicable to the detection of a signal in some element of a multiple-resolution-element radar is described. The procedure is based on rank-order statistics and is applicable to either a sequential or fixed-sample-size test; however, emphasis is placed on the sequential procedure. Results are given showing the expected sample size and probability of detection for the case of envelope detection (square-law or linear) of a fluctuating signal (Swerling model 2). A comparison is made with the optimum parametric sequential procedure.

Closed sequential tests of an exponential parameter

Abstract: SUMMARY This paper is concerned with the application of several closed sequential procedures to the testing of an exponential parameter. In particular, the procedures of Armitage (1957), Schneiderman & Armitage (1962a,b) and Anderson (1960) are considered. In certain of these cases either the properties or bounds on the properties of the sequential test can be obtained without approximations. There are certain situations in which the risk of a long sequential experiment is unacceptable. Some common examples are to be found in the area of medical trials and in various types of industrial experimentation. Such situations have brought about the study of alternatives to the sequential probability ratio test (SPRT) in which a procedure's boundaries are closed. One class of such tests is the 'restricted' procedures of Armitage (1957) and the 'wedge' plans of Schneiderman & Armitage (1962a, b). Another test which also belongs to this category is a modification of the SPRT as described by Anderson (1960) and by Donnelly in his unpublished Ph.D. thesis. These tests, which are concerned with normal means, require an approximation of the random walk by a diffusion process for an evaluation of their properties. In this paper we shall apply the above type regions to the testing of the parameter from an exponential distribution and show that in certain cases the properties of the test can be obtained without approximations.