CONCERNING ASYMPTOTIC NORMALITY OF A CLASS OF UNBIASED ESTIMATORS IN THE CASE OF ABSOLUTELY CONTINUOUS DISTRIBUTIONS

摘要

Let the following assumptions be satisfied: (A1) The observed random variable ξ has an absolutely continuous distribution with density f_θ (x); Eξ = a, Dξ = b~2 > 0, E|ξ|~3 < ∞. (A2) The distribution of the random variable ξ belongs to the one-parameter exponential distribution family that is defined by the expression f_θ(x) = g(x) exp{V_1(θ)x + V_2(θ)}, x ∈ R, where V_1(θ) and V_2(θ) are certain continuously differentiable functions of the parameter θ ∈ Θ is contained in R.