The Method of Moments

Abstract

Consider a family of distributions {¡ θ : θ ∈ Θ} and and consider a sample X = (X 1 ,. .. , X n) of i.i.d. random variables with distribution ¡ θ 0 , where θ 0 ∈ Θ. We assume that θ 0 is unknown and we want to construct an estimatê θ = ˆ θ n (X 1 , · · · , X n) of θ 0 based on the sample X. Let us recall some standard facts from probability that we be often used throughout this course.