Adaptive robust estimates of shift and scale parameters

摘要

An analysis of the radicalness criteria and robust estimation algorithms allows us to conclude that all these estimates can be derived based on the weighted maximum likelihood method (WMLM) with the estimation function of the form Φ(x,θ) = [(partial deriv)/(partial deriv θ) ln f (x,θ) + β] f~l (x,θ). In the present study, robust estimates of shifts and scales are synthesized in the class of Student's global supermodels and approximately normal distributions depending on the radicalness parameter l. Algorithms of adaptive robust estimates are suggested. They allow estimates to be adapted to distribution types and local deviations.