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August 1998 Regression-type inference in nonparametric autoregression
Jens-Peter Kreiss, Michael H. Neumann
Ann. Statist. 26(4): 1570-1613 (August 1998). DOI: 10.1214/aos/1024691254


We derive a strong approximation of a local polynomial estimator LPE in nonparametric autoregression by an (LPE) in a corresponding nonparametric regression model. This generally suggests the application of regression-typical tools for statistical inference in nonparametric autoregressive models. It provides an important simplification for the boot-strap method to be used: It is enough to mimic the structure of a nonparametric regression model rather than to imitate the more complicated process structure in the autoregressive case. As an example we consider a simple wild bootstrap, which is used for the construction of simultaneous confidence bands and nonparametric supremum-type tests.


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Jens-Peter Kreiss. Michael H. Neumann. "Regression-type inference in nonparametric autoregression." Ann. Statist. 26 (4) 1570 - 1613, August 1998.


Published: August 1998
First available in Project Euclid: 21 June 2002

zbMATH: 0935.62049
MathSciNet: MR1647701
Digital Object Identifier: 10.1214/aos/1024691254

Primary: 62G07, 62M05
Secondary: 62G09, 62G15

Rights: Copyright © 1998 Institute of Mathematical Statistics


Vol.26 • No. 4 • August 1998
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