Accession Number : AD0425901

Title :   ESTIMATING THE CURRENT MEAN OF A NORMAL DISTRIBUTION WHICH IS SUBJECTED TO CHANGES IN TIME,

Corporate Author : STANFORD UNIV CALIF

Personal Author(s) : Chernoff,H. ; Zacks,S.

Report Date : 31 OCT 1963

Pagination or Media Count : 42

Abstract : A tracking problem is considered. Observations are taken on the successive positions of an object traveling on a path, and it is desired to estimate its current position. The objective is to arrive at a simple formula which implicitly accounts for possible changes in direction and discounts observations taken before the latest change. To develop a reasonable procedure, a simpler problem is studied. Successive observations are taken on n independently and normally distributed random variables X sub 1, X sub 2, ..., X sub n with means mu sub 1, mu sub 2, ..., mu sub n and variance 1. Each mean mu sub i is equal to the preceding mean mu sub (i-1) except when an occasional change takes place. The object is to estimate the current mean mu sub n. This problem is studied from a Bayesian point of view. An 'ad hoc' estimator is described, which applies a combination of the A.M.O.C. Bayes estimator and a sequence of tests designed to locate the last time point of change. The various estimators are then compared by a Monte Carlo study of samples of size 9. This Bayesian approach seems to be more appropriate for the related problem of testing whether a change in mean has occurred. This test procedure is simpler than that used by Page. The power functions of the two procedures are compared. (Author)

Descriptors :   (*TRAJECTORIES, MATHEMATICAL PREDICTION), (*TRACKING, STATISTICAL DISTRIBUTIONS), TIME, PROBABILITY, STATISTICAL ANALYSIS, MONTE CARLO METHOD, DISTRIBUTION THEORY, DETERMINANTS(MATHEMATICS), ANALYSIS OF VARIANCE, STATISTICAL TESTS

Distribution Statement : APPROVED FOR PUBLIC RELEASE