The Lp-norm of a random variable with unknown distribution is determined by means of the substitution estimator. Under a mild moment condition, expansions of bias and variance are established.

This book presents the theory of probability and mathematical statistics at a level suitable for researchers at the frontiers of applied disciplines. Examples and exercises make essential concepts in measure theory and analysis accessible to those with preparation limited to vector calculus....

AbstractThe following sections are included:IntroductionIntegrationIntegrals on Abstract Measure SpacesIntegrals on Sets of Real NumbersProperties of E(·)Expectations as Informative FunctionalsMoments of Random VariablesGenerating FunctionsConditional ExpectationMoments of Conditional...