Accession Number : AD0668155

Title :   DENSITY ESTIMATION BY ORTHOGONAL SERIES.

Descriptive Note : Technical rept.,

Corporate Author : JOHNS HOPKINS UNIV BALTIMORE MD DEPT OF STATISTICS

Personal Author(s) : Watson,Geoffrey S.

Report Date : APR 1968

Pagination or Media Count : 7

Abstract : Given a random sample x sub 1...,x sub n from the density f(x) = Summation of (alpha sub m phi sub m(x)) where (braces) phi sub m(x) is an orthogonal basis, the estimator f star sub n(x) = Summation from zero to infinity of (lambda sub m(n) a sub m phi sub m(x)) where a sub m = (1/n) Summation from k = 1 to k = n, of phi sub m(x sub k) is suggested. f star sub n(x) will be a minimum integrated mean square error estimator in its class. These estimators are related to the kernel estimators discussed by Watson and Leadbetter (Ann. Math. Statist. 1963, 34, 480-491.).

Descriptors :   (*PROBABILITY DENSITY FUNCTIONS, SERIES(MATHEMATICS)), SAMPLING, FUNCTIONS(MATHEMATICS), STATISTICAL DISTRIBUTIONS

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE