On ARMA Probability Density Estimation.
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 f(p,q)(.), p= 0,1,2,... and q = 0,1,2,..., which are such that f(O,q)(.) is a Fourier series (Kronmal-Tarter type) estimator and f(p,O)(.) is an autoregressive estimator. Each of the estimators f(p.q.)(.) (referred to as ARMA estimators) is shown to depend upon the e(n)-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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1981
- Accession Number
- ADA109638
Entities
People
- Henry L. Gray
- Jeffrey D. Hart
Organizations
- Southern Methodist University