ABSTRACT
The likelihood admits a representation in terms of the intensity processes. This chapter provides conditions for uniform local asymptotic normality and consider the problem of constructing efficient estimators for functional of the parameter. The standardized error of a regular and asymptotically efficient estimator is stochastically approximable by the derivative of the likelihood in the direction least favorable for the functional. The chapter shows how the characterization can be used to prove efficiency for certain martingale estimators, an infinite-dimensional version of the Newton–Raphson improvement of a preliminary estimator, solutions of estimating equations based on derivatives of the likelihood, including nonparametric maximum likelihood estimators. Uniform local asymptotic normality and expansion rely on a number of regularity conditions.
