Moments of a Random Vector and of Linear and Quadratic Forms in a Random Vector

Abstract

A considerable body of theory on point estimation of the parameters of linear models can be obtained using only some results pertaining to the first few moments of a random vector and of certain functions of that vector; it is not necessary to specify the random vector’s probability distribution. This chapter presents these moment results. In the first section, moments up to fourth order (mean vector, variance–covariance matrix, skewness matrix, and kurtosis matrix) are defined. In the second section, moments (up to second order) of linear and quadratic forms in a random vector are derived in terms of the moments (up to fourth order) of the random vector.