Abstract
A derivation of the joint probability distribution and mass functions of order statistics coming from overlapping samples is presented. The general formulation allows for samples of any size overlapping (coinciding) in any number of observed values ranging from zero to the number of observations in the smaller sample. These expressions are used to compute the autocovariance function of a moving L-estimate (linear combination of order statistics) of a sequence of independent, identically distributed second-order random variables, under a variety of assumptions on the parent distribution. The associated variance spectral density is also computed for several filters of interest, including median filters, and inner and outer trimmed mean filters.
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