Rates of convergence in the asymptotic normality for some local maximum estimators (original) (raw)

This paper explores the rates of convergence in the context of asymptotic normality for local maximum estimators, building on recent advancements in the theory of probability in Banach spaces and empirical processes. It illustrates how conditions involving stochastic differentiability and Taylor expansion can be employed to establish a connection between the asymptotic properties of estimators and their convergence rates. Key results provide insight into the necessary conditions for convergence, emphasizing the importance of specifying the right forms of convergence for practical applications in mathematical statistics.