Showing papers on "Sequential probability ratio test published in 1972"

Sequential Sampling Plans for the Bollworm, Heliothis zea

Abstract: A sequential decision plan based on the sequential probability ratio test has been derived for determining the infestation status of Heliothis zea (Boddie) in cotton. In addition, a sequential counting or estimation plan has also been derived for fixing the coefficient of variation of the mean. Both of these plans are based on 3 years of data from 5 different untreated cotton fields in the San Joaquin Valley of California. Our general findings based on computer calculations and field trials follow: (1) Five adjacent cotton plants have been found to be a preferable sampling unit to 1- or 3-plant sample units in a sequential decision plan. Although a slight advantage exists in smaller sample units in terms of total plants required, the increased amount of walking between the larger number of small units more than offsets any advantage. (2) If 50 plants per 20 acres arc taken as a practical limit on sampling, up to 25% chance of error must he tolerated in a test of 8 vs. 15 worms/100 plants. Up to 20% chance of error must he tolerated in a test of 10 vs. 20 worms/100 plants. (3) The sequential decision plan agrees well with previous methods (12 5-plant samples) with only one disagreement out of 40 comparisons. In addition, good agreement between predicted and observed sampling requirements was found. (4) Sampling distributions for the cotton bollworm have the characteristic that the sample variance increases more rapidly than the mean. This suggests a clustered spatial pattern and is in wide agreement with the literature. (5) In a sequential counting plan which fixes C, the standard error to mean ratio, very high sampling requirements are indicated at low population means.

Likelihood ratio tests for sequential k-decision problems

Abstract: Sequential tests of separated hypotheses concerning the parameter θ of a Koopman-Darmois family are studied from the point of view of minimizing expected sample sizes pointwise in θ subject to error probability bounds. Sequential versions of the (generalized) likelihood ratio test are shown to exceed the minimum expected sample sizes by at most M log log α(-1) uniformly in θ, where α is the smallest error probability bound. The proof considers the likelihood ratio tests as ensembles of sequential probability ratio tests and compares them with alternative procedures by constructing alternative ensembles, applying a simple inequality of Wald and a new inequality of similar type. A heuristic approximation is given for the error probabilities of likelihood ratio tests, which provides an upper bound in the case of a normal mean.

Sequential Comparison of Exponential Survival Curves

Abstract: A general approach is outlined to the problem of sequentially comparing exponential “survival” curves in a clinical trials setting. It entails applying sequential tests of hypotheses concerning the drift of a Wiener process to a particular discrete-time process generated from the survival data. Anderson's [1] modified sequential probability ratio test [SPRT) is used for illustration. Monte Carlo studies indicate that the method is valid for samples of moderate size and that it may result in considerable savings of observations compared with the widely used sequential sign test. Though the results are presented in the language of clinical trials, applications to life-testing and reliability problems may be envisaged.

A Sequential Probability Ratio Test for Availability

Abstract: System availability is an important measure of system effectiveness This is particularly true of systems which are required to be “on station” more or less continuously, eg, early warning systems, patrol craft and others This paper presents a Generalized Sequential Probability Ratio Test (GSPRT) of the hypothesis where A = θ/(θ + ϕ) and θ, ϕ are means of the exponential distributions of failure and repair times respectively The ASN and O C curves are discussed In addition, termination is shown and examples are given The availability, defined above, is a point availability and if logistics and administrative delays are excluded from restoration time, it is often called inherent availability; otherwise, it is called operational availability

Sequential tests to select among M hypotheses (Corresp.)

Abstract: Suboptimal stopping rules are developed for the sequential detection of one of M orthogonal signals. One procedure is derived from the information measures associated with sequential probability ratio tests (SPRTs). The resultant stopping rules are relatively simple functions of M and the error probabilities desired for the sequential tests.

Linear sequential pattern classification (Corresp.)

Abstract: A nonparametric sequential pattern classifier called a linear sequential classifier (LSC) is presented. The pattern components are measured sequentially and the decisions either to measure the next component or to stop and classify the pattern are made using linear functions derived from sample patterns based on the least mean-square error criterion. The required linear functions are computed using an adaption of Greville's recursive algorithm for computing the generalized inverse of a matrix. A recursive algorithm for computing the least mean-square error is given and is used to determine the order in which the pattern components are measured. Under the assumption of two equiprobable classes that are normally distributed with equal covariance matrices, it is shown that the LSC is equivalent to Wald's sequential probability ratio test. Computer-simulated experiments indicate that the LSC is more effective than existing nonparametric sequential classifiers.

On a wald's equation and average sample number in a sequential signal detection

Abstract: It is shown that in detecting sequentially a deterministic signal 0(0 in white noise 72(0 a similar identity (iii) in theorem 2.1, to the Wald's holds concerning a stopping time r determined by making use of a likelihood ratio. It is also shown that r has finite moments of any order under quite weak conditions over the signal. The exact A. S. N. E{y} in a constant signal case has been obtained and given by (2, 8). It is also considered a detection problem of a constant signal OW a in a coloured noise based on a sub-optimal statistic which become optimal when the noise were white. Similar properties of a stopping time r to those in the white noise case have been obtained in theorem 3.1.