Comparison of Parametric and Empirical Likelihood Functions
本文比较了参数似然函数和经验似然函数，推导了非参数和参数情形下对数似然函数的一阶和二阶展开，并给出了两者差异的精确阶数。
In this paper, parametric and empirical likelihood functions or surfaces are compared. In particular, first- and second-order expansions for log likelihood functions are developed in nonparametric and parametric situations, where the functional of interest is a smooth function of vector means. The two approaches are compared and the precise order of difference between the nonparametric and parametric log likelihood functions is obtained. In general, the surfaces need not agree to first order. However, in certain exponential family models, the surfaces are quite close in a distributional sense. Moreover, empirical likelihood can be thought of as an approximation to a true parametric likelihood based on a parametric least favourable family.