Nonparametric regression with long-range dependence
The effect of dependent errors in fixed-design, nonparametric regression is investigated. It is shown that convergence rates for a regression mean estimator under the assumption of independent errors are maintained in the presence of stationary dependent errors, if and only if [Sigma] r(j) < [infinity], where r is the covariance function. Convergence rates when [Sigma] r(j) = [infinity] are also investigated. In particular, when the sample is of size n, when the mean function has k derivatives and r(j) ~ Cj-[alpha], the rate is n-k[alpha]/(2k+[alpha]) for 0 < [alpha] < 1 and (n-1 log n)k/(2k+1) for [alpha] = 1. These results refer to optimal convergence rates. It is shown that the optimal rates are achieved by kernel estimators.
Year of publication: |
1990
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Authors: | Hall, Peter ; Hart, Jeffrey D. |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 36.1990, 2, p. 339-351
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Publisher: |
Elsevier |
Keywords: | autoregression convergence rate long-range dependence moving average nonparametric regression |
Saved in:
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