Accession Number : AD0264811

Title :   ON THE ESTIMATION OF THE PROBABILITY DENSITY

Corporate Author : RESEARCH TRIANGLE INST DURHAM N C

Personal Author(s) : LEADBETTER,M.R. ; WATSON,G.S.

Report Date : 02 SEP 1961

Pagination or Media Count : 1

Abstract : Estimators of the form fn(x) = 1-n ni=1 n(x-xi), of a probability density f(x) are considered, where x1,...., xn is a sample of n observations from f(x). The properties of such estimators are discussed on the basis of their mean integrated square errors, E (fn(x) - f(x))2dx (M.I.S.E.), and also on the basis of various pointwise consistency criteria. The corresponding development for discrete distributions is sketched and examples are given in both continuous and discrete cases. The definitions and results are analogous to those of Parzen for the spectral density. (Author)

Descriptors :   *DENSITY, *PROBABILITY, ALGEBRA, DISTRIBUTION THEORY, EQUATIONS, FUNCTIONS(MATHEMATICS), INTEGRAL EQUATIONS, SAMPLING, STATISTICAL ANALYSIS, THEORY

Distribution Statement : APPROVED FOR PUBLIC RELEASE