21 April 2006 Nonparametric robust estimates of the shift and scale parameters
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Proceedings Volume 6160, Twelfth Joint International Symposium on Atmospheric and Ocean Optics/Atmospheric Physics; 61600Z (2006) https://doi.org/10.1117/12.675243
Event: Twelfth Joint International Symposium on Atmospheric and Ocean Optics/Atmospheric Physics, 2005, Tomsk, Russian Federation
Abstract
In the present study, a class of nonparametric robust estimates of the shift and scale parameters (μ, S) of the form (please see manuscript for formula) is synthesized by the weighted maximum likelihood method based on parametric density estimates, where (see manuscript for formula) are the Walsh half-sums, K(u) is the kernel function, and W(u) is the weighting function: (see formula in manuscript.) The radicalness parameter I determines the weighting functions W(zij) executing the process of soft truncation of the estimates depending on a priori information on outliers: the estimates converge to maximum likelihood estimates (MLE) at l = 1 and to radical estimates at l = 0.5. The adaptive estimates converge to radical ones. They belong to the class of nonparametric estimates of implicit parameters, and their study is performed based on the generalized M-estimates.
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I. V. Rymar, V. A. Simakhin, "Nonparametric robust estimates of the shift and scale parameters", Proc. SPIE 6160, Twelfth Joint International Symposium on Atmospheric and Ocean Optics/Atmospheric Physics, 61600Z (21 April 2006); doi: 10.1117/12.675243; https://doi.org/10.1117/12.675243
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