Accession Number:

ADA109638

Title:

On ARMA Probability Density Estimation.

Descriptive Note:

Technical rept.,

Corporate Author:

SOUTHERN METHODIST UNIV DALLAS TEX DEPT OF STATISTICS

Personal Author(s):

Report Date:

1981-12-01

Pagination or Media Count:

130.0

Abstract:

A new method of probability density estimation is investigated which exploits the Fourier series representation of a density function. The new method employs density estimators fp,q., p 0,1,2,... and q 0,1,2,..., which are such that fO,q. is a Fourier series Kronmal-Tarter type estimator and fp,O. is an autoregressive estimator. Each of the estimators fp.q.. referred to as ARMA estimators is shown to depend upon the en-transform, thus providing a strong motivation for the use of estimators with both p O and q O. Small and large sample properties of ARMA density estimators are obtained and a data-based method of selecting optimal values of p and q is proposed. The results of a simulation study show that, for the densities considered, a savings in integrated square error is attained by using ARMA, rather than Fourier series, density estimation.

Subject Categories:

  • Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE