A Comparison between Parametric and non-parametric Density Estimation based on LCV Variance Estimation

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Sayyareh Abdolreza

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Journal Paper

Paper Information

Journal: Journal of the Iranian Statistical Society Year:2023 | Volume:22 | Issue:1 Page(s): 1-27

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Information Journal Paper

Title

A Comparison between Parametric and non-parametric Density Estimation based on LCV Variance Estimation

Author(s)

Sayyareh Abdolreza | Issue Writer Certificate

Keywords

Akaike Information Criterion

Kernel density

Likelihood Cross-validation

Time Series

tracking interval

Vuong's Test

Abstract

When the parametric model does not hold, and we cannot fit a parametric model to the data, the true density may be estimated non-parametrically, as in the case of a kernel estimate. The purpose of this paper is to present a comparison between parametric and non-parametric models. The parametric investigation contains Vuong's Test, and tracking interval based on the known maximum likelihood estimation theory. The presented non-parametric analysis involves Kernel density estimation. Modified differences of Kullback-Leibler criteria between two rival models and Vuong's Test, have been considered. In this circumstance, we address the problem of cross-validation estimation of variance for Kullback-Leibler divergence between the true but unknown density and its kernel estimator. A simulation study and data analysis have shown that the parametric density is a more realistic estimate of the data generating density.

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