On ARMA Probability Density Estimation.
SOUTHERN METHODIST UNIV DALLAS TEX DEPT OF STATISTICS
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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.
- Statistics and Probability