Transformation Kernel Density Estimation With Applications
| Autor: | Gerhard Koekemoer, Jan W. H. Swanepoel |
|---|---|
| Rok vydání: | 2008 |
| Předmět: |
Statistics and Probability
Mathematical optimization Kernel density estimation Estimator Multivariate kernel density estimation Semiparametric model Transformation (function) Variable kernel density estimation Kernel (statistics) Discrete Mathematics and Combinatorics Applied mathematics Semiparametric regression Statistics Probability and Uncertainty Mathematics |
| Zdroj: | Journal of Computational and Graphical Statistics. 17:750-769 |
| ISSN: | 1537-2715 1061-8600 |
| Popis: | One of the main objectives of this article is to derive efficient nonparametric estimators for an unknown density fX. It is well known that the ordinary kernel density estimator has, despite several good properties, some serious drawbacks. For example, it suffers from boundary bias and it also exhibits spurious bumps in the tails. We propose a semiparametric transformation kernel density estimator to overcome these defects. It is based on a new semiparametric transformation function that transforms data to normality. A generalized bandwidth adaptation procedure is also developed. It is found that the newly proposed semiparametric transformation kernel density estimator performs well for unimodal, low, and high kurtosis densities. Moreover, it detects and estimates densities with excessive curvature (e.g., modes and valleys) more effectively than existing procedures. In conclusion, practical examples based on real-life data are presented. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|