Accession Number : ADA114623

Title :   Some Penalized Likelihood Procedures for Smoothing Probability Densities.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Atilgan,Taskin ; Leonard,Tom

PDF Url : ADA114623

Report Date : Feb 1982

Pagination or Media Count : 25

Abstract : Some methods are considered for the estimation of probability densities. They employ a linear approximation to either the density or the logistic density transform. The coefficients in the approximation are estimated by maximum likelihood and the number of terms is judged via an information criterion. Hence the traditionally difficult problem of judging the degree of smoothness is carried out in a relatively simple manner. Criteria considered include the penalties proposed by Akaike and Schwarz for model complexity, together with an empirical criterion based upon a plot of the log-likelihoods. The practical procedures are related to an asymptotic consistency argument and a number of numerical examples are presented.

Descriptors :   *Probability density functions, *Estimates, *Approximation(Mathematics), Logistics, Transformations(Mathematics), Information processing, Standards, Parametric analysis, Histograms, Consistency, Asymptotic series, Penalties, Coefficients

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE