New approaches to nonparametric density estimation and selection of smoothing parameters

Golyandina, Nina, Pepelyshev, Andrey ORCID: https://orcid.org/0000-0001-5634-5559 and Steland, Ansgar 2012. New approaches to nonparametric density estimation and selection of smoothing parameters. Computational Statistics & Data Analysis 56 (7) , pp. 2206-2218. 10.1016/j.csda.2011.12.019

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Abstract

The application of Singular Spectrum Analysis (SSA) to the empirical distribution function sampled at a grid of points spanning the range of the sample leads to a novel and promising method for the computer-intensive nonparametric estimation of both the distribution function and the density function. SSA yields a data-adaptive filter, whose length is a parameter that controls the smoothness of the filtered series. A data-adaptive algorithm for the automatic selection of a general smoothing parameter is introduced, which controls the number of modes of the estimated density. Extensive computer simulations demonstrate that the new automatic bandwidth selector improves on other popular methods for various densities of interest. A general uniform error bound is proved for the proposed SSA estimate of the distribution function, which ensures its uniform consistency. The simulation results indicate that the SSA density estimate with the automatic choice of the filter length outperforms the kernel density estimate in terms of the mean integrated squared error and the Kolmogorov–Smirnov distance for various density shapes. Two applications to problems arising in photovoltaic quality control and economic market research are studied to illustrate the benefits of SSA estimation.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	Empirical distribution function; Time series smoothing; Singular Spectrum Analysis; Adaptive filter; Acceptance sampling plans
Publisher:	Elsevier
ISSN:	0167-9473
Last Modified:	24 Oct 2022 11:42
URI:	https://orca.cardiff.ac.uk/id/eprint/49044

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