Nonparametric estimation of a regression function

Autor:	Kuang-Fu Cheng, Pi-Erh Lin
Rok vydání:	1981
Předmět:	Statistics and Probability General Mathematics Regression function Uniform convergence Order (ring theory) Interval (mathematics) Function (mathematics) Lipschitz continuity Combinatorics Monotone polygon Statistics Statistics Probability and Uncertainty Random variable Analysis Mathematics
Zdroj:	Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete. 57:223-233
ISSN:	1432-2064 0044-3719
DOI:	10.1007/bf00535491
Popis:	Consider the regression model Yi*=g(xi*)+ei*, i=1,2,...,n, where xi*'s denote unordered design variables, and g is an unknown function defined on the interval [0,1]. Assume {ei*} are iid random variables with zero mean and finite variance. Priestley and Chao (1972) and Clark (1977) proposed estimators g2nand g3n, respectively for g. In this paper, the asymptotic behavior of g2nand g3nis studied utilizing the properties of the new estimator g1n. It is shown that g1n, g2n, g3nare asymptotically equivalent in various senses. Moreover, consistency results are established and rates of uniform convergence obtained. For example, if E¦e*¦3
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::56c9956750bd211982d187db7a87866a https://doi.org/10.1007/bf00535491 Zobrazit plný text záznamu Full text from SpringerLink