Optimal designs for nonparametric kernel regression |
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Authors: | Hans-Georg Müller |
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Institution: | Institut für Medizinisch-Biologische Statistik und Dokumentation der Philipps-Universität Marburg, Ernst-Giller-Strasse 20, 3550 Marburg/L., FRG |
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Abstract: | We consider the fixed design regression model Yi = g(ti) + ξi, i = 1, …, n, where ξi are (not necessarily i.i.d.) no variables, ti constitute the design points where nonrepeatable measurements are to be taken and Yi are the observations from which g and its derivatives are to be estimated. The dependency of the Integrated Mean Squared Error of two different types of kernel estimates on the design {t1, …, tn} is established. This allows the derivation of asymptotically optimal designs. |
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Keywords: | 62K05 62G05 62J06 65D10 nonparametric regression fixed design design density kernel estimates of derivatives locally varying bandwidth |
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