A study of the effectiveness of simple density estimation methods (Q1965931)

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.