consistent estimation of the density of residuals in random design regression models

Autor:	Michael Kohler, Tina Felber, Adam Krzyżak, Luc Devroye
Rok vydání:	2012
Předmět:	Statistics and Probability Kernel density estimation Statistics Regression analysis Density estimation Statistics Probability and Uncertainty Studentized residual Particle density Regression Multivariate kernel density estimation Nonparametric regression Mathematics
Zdroj:	Statistics & Probability Letters. 82:173-179
ISSN:	0167-7152
DOI:	10.1016/j.spl.2011.09.023
Popis:	In this paper we study the problem of estimating the density of the error distribution in a random design regression model, where the error is assumed to be independent of the design variable. Our main result is that the L 1 error of the kernel density estimate applied to residuals of a consistent regression estimate converges with probability 1 to 0 regardless of the form of the true density. We demonstrate that this result is in general no longer true if the error distribution and the design variable are dependent.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::6d20b411f37596f229e50366edc5a379 https://doi.org/10.1016/j.spl.2011.09.023 Zobrazit plný text záznamu Full Text from ScienceDirect