Abstract #300637

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JSM 2003 Abstract #300637
Activity Number: 56
Type: Contributed
Date/Time: Sunday, August 3, 2003 : 4:00 PM to 5:50 PM
Sponsor: Section on Nonparametric Statistics
Abstract - #300637
Title: A Comparative Analysis of Theoretical and Empirical Measures of Fitting and Smoothing for Several Restricted Function Estimators
Author(s): Estela Bee Dagum*+ and Alessandra Luati
Companies: University of Bologna and University of Bologna
Address: Dept. of Statistics, Ottawa, ON, K1N6K6, Canada
Keywords: loess ; cubic smoothing spline ; Gaussian kernel ; 13-term Henderson filter ; symmetric and asymmetric filters
Abstract:

We calculate theoretical measures of fitting and smoothing for several nonparametric function estimators on the basis of their symmetric and asymmetric weight systems. The function estimators discussed, namely Loess of degree 1 and 2, the cubic smoothing spline and the Gaussian kernel, are all restricted to a fixed length of 13 terms. We aim to evaluate their properties for nonstationary mean estimation (trend-cycle) in the context of current socioeconomic analysis. All the measures are standardized by those given by the 13-term Henderson filter, widely applied in time series decomposition. For each restricted function estimator, we also calculate empirical measures of fitting and smoothing for a large sample of real series characterized by different degrees of variability. The results show that the theoretical smoothing measures are in agreement with the empirical ones. Similarly, the theoretical fitting measure analyzed in terms of bias and variance composition, provides sound information on the smoothers' symmetric filters fit given by their empirical MSEs. For the asymmetric filters, the above analysis must be done jointly with their theoretical smoothing measures.

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