A study of the effectiveness of simple density estimation methods
type: Item
instance of: scholarly article
title: A study of the effectiveness of simple density estimation methods
zbMATH Open document ID: 0936.62041
author: Jeffrey S. Simonoff
author: Clifford Hurvich
published in: Computational Statistics
publication date: 2000-03-02T00:00:00Z
review text: With the help of Monte Carlo simulation the effectiveness of simple spectral density estimates (including the histogram and frequency polygon) are examined for different methods of data range partitions: Gaussian-based; oversmoothed; cross-validation with fixed bins; partitions of locally equalized cells (POLEC) -- the authors' algorithm based on a paper by \textit{A. Kogure} [Ann. Stat. 15, 1023-1030 (1987; Zbl 0631.62049)]. The integrated squared error \(ISE(\hat f)=\int(\hat f(x) - f(x))^2dx\) and the relative integrated squared error \(RISE(\hat f)=\int(\hat f(x) - f(x))^2/f(x)dx\) are used as measures of efficiency. Simulated samples from the Gaussian, lognormal, exponential, \(t(3)\), Gaussian mixtures and beta distributions of size from 20 to 500 and some examples of real data are used to investigate the behavior of the estimators. The authors concluded that the POLEC and Gaussian-based partition algorithms are quite effective.
Mathematics Subject Classification ID: 62G07
Mathematics Subject Classification ID: 65C05
zbMATH DE Number: 1409658
zbMATH Keywords: frequency polygon
zbMATH Keywords: histogram
zbMATH Keywords: bandwidth selection
zbMATH Keywords: cross-validation
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1409658