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Titolo:
Nonparametric regression with dependent errors
Autore:
Yang, YH;
Indirizzi:
Iowa State Univ, Dept Stat, Ames, IA 50011 USA Iowa State Univ Ames IA USA 50011 ate Univ, Dept Stat, Ames, IA 50011 USA
Titolo Testata:
BERNOULLI
fascicolo: 4, volume: 7, anno: 2001,
pagine: 633 - 655
SICI:
1350-7265(200108)7:4<633:NRWDE>2.0.ZU;2-T
Fonte:
ISI
Lingua:
ENG
Soggetto:
LONG-RANGE DEPENDENCE; QUADRATIC-FORMS; VARIABLES;
Keywords:
long-range dependent errors; minimax rate of convergence; nonparametric regression;
Tipo documento:
Article
Natura:
Periodico
Settore Disciplinare:
Physical, Chemical & Earth Sciences
Citazioni:
35
Recensione:
Indirizzi per estratti:
Indirizzo: Yang, YH Iowa State Univ, Dept Stat, Ames, IA 50011 USA Iowa State Univ Ames IA USA 50011 Dept Stat, Ames, IA 50011 USA
Citazione:
Y.H. Yang, "Nonparametric regression with dependent errors", BERNOULLI, 7(4), 2001, pp. 633-655

Abstract

We study minimax rates of convergence for nonparametric regression under arandom design with dependent errors. It is shown that when the errors are independent of the explanatory variables, long-range dependence among the errors does not necessarily hurt regression estimation, which at first glance contradicts earlier results by Hall and Hart, Wang, and Johnstone and Silverman under a fixed design. In fact we show that, in general, the minimax rate of convergence under the square L-2 loss is simply at the worse of twoquantities: one determined by the massiveness of the class alone and the other by the severity of the dependence among the errors alone. The clear separation of the effects of the function class and dependence among the errors in determining the minimax rate of convergence is somewhat surprising. Examples of function classes under different covariance structures includingboth short- and long-range dependences are given.

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Documento generato il 29/05/20 alle ore 17:03:44