Applications of Anova Type Decompositions for Comparisons of Conditional Variance Statistics Including Jackknife Estimates

Abstract

Variance and bias comparisons are set forth for a sequence of nonlinear statistics based on independent random variables including jackknife and U-statistics of various orders. The analysis relies heavily on an orthogonal decomposition first introduced by Hoeffding in 1948. This ANOVA type decomposition is refined for purposes of discerning higher order convexity properties for an array of conditional variance coefficients. There is also some discussion of two-sample statistics.