Stochastic Differentiability in Maximum Likelihood Theory
Vladimir Dobrić, Cathy Liebars · Birkhäuser Boston eBooks · 1994
In the classical asymptotic likelihood theory, there exists a vast number of results concerning asymptotic normality of maximum likelihood estimators (see for example [2]). Proofs in asymptotic maximum theory begin with a careful application of Taylor’s theorem. In the past, generalizations were focused on weakening conditions on the remainder term (for example, LeCam [3]). In the last ten years, the remainder term has been treated stochastically by Pollard (1984) and Hoffmann-Jorgensen (1990). Based on the most recent developments in the theory of infinite dimensional laws of large numbers and infinite dimensional central limit theorems, Pollard [4] has condensed many of the technicalities that arise in the asymptotic normality of maximum estimators into a single stochastic equicontinuity condition imposed on a remainder term. These generalizations have been pursued further by Hoffmann-Jorgensen [1] who developed the idea of stochastic differentiability which requires that a remainder term satisfies an even weaker condition than stochastic equicontinuity. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.