Representations of moments using lower-order conditional moments
Journal
Journal of Statistical Planning and Inference
Date Issued
2007
Author(s)
DOI
10.1016/j.jspi.2005.11.001
Abstract
Moments and central moments of a random variable X are expressed as integrals of functions of lower-order conditional moments and the cumulative distribution of X. In particular, sample central moments of order 2 k are expressed as the sum of between groups variations, providing an analogue to the analysis of variance. Similar expressions are obtained for the expectations of real-valued and measurable functions of X.
Subjects