Uniformly best estimation in linear regression when prior information is fuzzy

Autor:	Peter Stahlecker, Bernhard F. Arnold
Rok vydání:	2009
Předmět:	Statistics and Probability Mathematical optimization Mean squared error Fuzzy set Linear regression Applied mathematics Estimator Generalized least squares Affine transformation Statistics Probability and Uncertainty Fuzzy logic Ellipsoid Mathematics
Zdroj:	Statistical Papers. 51:485-496
ISSN:	1613-9798 0932-5026
DOI:	10.1007/s00362-009-0222-z
Popis:	Modeling prior information as a fuzzy set and using Zadeh’s extension principle, a general approach is presented how to rate linear affine estimators in linear regression. This general approach is applied to fuzzy prior information sets given by ellipsoidal α-cuts. Here, in an important and meaningful subclass, a uniformly best linear affine estimator can be determined explicitly. Surprisingly, such a uniformly best linear affine estimator is optimal with respect to a corresponding relative squared error approach. Two illustrative special cases are discussed, where a generalized least squares estimator on the one hand and a general ridge or Kuks–Olman estimator on the other hand turn out to be uniformly best.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::4ec90cb8125edc6c5c5b9e43c124eea3 https://doi.org/10.1007/s00362-009-0222-z Zobrazit plný text záznamu Full text from SpringerLink