# 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.

# Descriptors:

# Subject Categories:

- Statistics and Probability