Kaiserslautern - Fachbereich Mathematik
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Mrázek et al. [14] proposed a unified approach to curve estimation which combines
localization and regularization. In this thesis we will use their approach to study
some asymptotic properties of local smoothers with regularization. In Particular, we
shall discuss the regularized local least squares (RLLS) estimate with correlated errors
(more precisely with stationary time series errors), and then based on this approach
we will discuss the case when the kernel function is dirac function and compare our
smoother with the spline smoother. Finally, we will do some simulation study.
Mrázek et al. [25] proposed a unified approach to curve estimation which combines localization and regularization. Franke et al. [10] used that approach to discuss the case of the regularized local least-squares (RLLS) estimate. In this thesis we will use the unified approach of Mrázek et al. to study some asymptotic properties of local smoothers with regularization. In particular, we shall discuss the Huber M-estimate and its limiting cases towards the L2 and the L1 cases. For the regularization part, we will use quadratic regularization. Then, we will define a more general class of regularization functions. Finally, we will do a Monte Carlo simulation study to compare different types of estimates.