ABSTRACT
Certain important statistical problems have the following form. Let X 1, X 2,… be a sequence of i.i.d. random variables with common distribution function F(x), and let U(x, θ) be a measurable function of x for all θ in some parameter space Θ. The statistic of interest for purposes of estimation or testing hypotheses is https://www.w3.org/1998/Math/MathML"> ( 1 / n ) ∑ i = 1 n U ( X i , θ ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315136288/c12c5089-77f8-4e14-84a1-364a5e26ae30/content/eq797.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> . If it is assumed that () https://www.w3.org/1998/Math/MathML"> μ ( θ ) = E U ( X , θ ) = ∫ U ( x , θ ) d F ( x ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315136288/c12c5089-77f8-4e14-84a1-364a5e26ae30/content/eq798.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>
