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Neumann, Michael H.; Kreiss, Jens-Peter

Regression-type inference in nonparametric autoregression. (English) Zbl 0935.62049

Ann. Stat. 26, No. 4, 1570-1613 (1998).
Summary: 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 bootstrap 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.

Cited in 38 Documents

MSC:

62G08 Nonparametric regression and quantile regression
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G09 Nonparametric statistical resampling methods

Keywords:

bootstrap; strong approximation; nonparametric autoregression; nonparametric regression; wild bootstrap; confidence bands
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References:

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