Showing papers by "Frits H. Ruymgaart published in 2002"
TL;DR: In this paper, the van trees inequality is applied to obtain lower bounds for the quadratic risk of estimators for the variance function and its derivatives in non-parametric regression models.
Abstract: In this paper the van Trees inequality is applied to obtain lower bounds for the quadratic risk of estimators for the variance function and its derivatives in non–parametric regression models. This approach yields a much simpler proof compared to previously applied methods for minimax rates. Furthermore, the informative properties of the van Trees inequality reveal why the optimal rates for estimating the variance are not affected by the smoothness of the signal g. A Fourier series estimator is constructed which achieves the optimal rates. Finally, a second–order correction is derived which suggests that the initial estimator of g must be undersmoothed for the estimation of the variance.
10 citations
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TL;DR: In this paper, the authors discuss a procedure to improve the usual estimator of a linear functional of the unknown regression function in inverse nonparametric regression models, and present a self-contained proof of the asymptotic efficiency.
Abstract: In this paper we will discuss a procedure to improve the usual estimator of a linear functional of the unknown regression function in inverse nonparametric regression models. In Klaassen, Lee, and Ruymgaart (2001) it has been proved that this traditional estimator is not asymptotically efficient (in the sense of the H\'{a}jek - Le Cam convolution theorem) except, possibly, when the error distribution is normal. Since this estimator, however, is still root-n consistent a procedure in Bickel, Klaassen, Ritov, and Wellner (1993) applies to construct a modification which is asymptotically efficient. A self-contained proof of the asymptotic efficiency is included.
6 citations
01 Jan 2002
TL;DR: LocLocally dependent processes as mentioned in this paper are (m − 1) dependent (m ∈ N) processes where m is allowed to increase with the sample size n. Although locally dependent processes are of independent interest, they also appear as a tool in the asymptotic study of linear processes and processes of similar decomposable structure.
Abstract: Locally dependent processes are (m − 1) dependent (m ∈ N) processes where m is allowed to increase with the sample size n. Versions of such processes have been regularly studied in the literature. Although locally dependent processes are of independent interest, they also appear as a tool in the asymptotic study of linear processes and processes of similar decomposable structure.
1 citations