Accession Number : AD0696072

Title :   A CHI-SQUARE STATISTIC WITH RANDOM CELL BOUNDARIES.

Descriptive Note : Technical rept.,

Corporate Author : PURDUE UNIV LAFAYETTE IND DEPT OF STATISTICS

Personal Author(s) : Moore,David S.

Report Date : OCT 1969

Pagination or Media Count : 22

Abstract : Given a family F(x1 theta) of sufficiently smooth distributions in k-dimensional space depending on an m-dimensional parameter theta, estimate theta by an asymptotically efficient estimator theta prime. Define a chi-square statistic on random cells whose boundaries depend on theta prime. The asymptotic distribution of such statistics is obtained, generalizing work of A. R. Roy for k=1. The limiting distribution depends on theta in general, but is independent of theta for location and location-scale families. Moreover, the distribution approaches chi square (M-m-1) as the number of cells M approaches infinity. A table of upper critical points is given for several values of M for the case where F(x1 theta) is univariate normal. This should be useful in testing goodness of fit to the normal family. (Author)

Descriptors :   (*STATISTICAL DISTRIBUTIONS, DECISION THEORY), STATISTICAL TESTS, ANALYSIS OF VARIANCE, SAMPLING, THEOREMS

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE