Order Statistic Filtering and Smoothing of Time Series Part II
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چکیده
This is the second paper of a two part tutorial on the fundamentals of univariate time series ltering using order statistics where both temporal and rank orderings are considered jointly This second paper focuses on order statistic selection lters where the lter output is restricted to be one of the input samples In particular we treat class of Weighted Order Statistic WOS lters and the more generalized lter class of Permutation Weighted Order Statistic PWOS lters By combining temporal and rank order based weighting with order statistic selection detail and edge preserving lters that are robust to outliers and sample contamination can be constructed Like their weighted sum counterparts these selection lters can be applied to the smoothing ltering and forecasting of time series Furthermore selection lters can be optimized as a function of the underlying signal statistics While the weighted sum lter optimization is formulated under the Mean Squared Error the selection lters utilize the more robust Mean Absolute Error MAE criteria This MAE optimization and selection based estimates results in a robust class of lters that has advantages over the weighted sum counterparts in many applications The evolution of these lters is covered and illustrative examples are given demonstrating the properties and performance of this class of estimators Invited paper to appear in the Handbook of Statistics Order Statistics and Their Applications C R Rao and N Balakrishnan Editors BARNER AND ARCE CONTENTS
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تاریخ انتشار 2005