Martingale central limit theorems without uniform asymptotic negligibility: Corrigendum
نویسندگان
چکیده
منابع مشابه
General Central Limit Theorems Via Negligibility
The central limit theorem (CLT) for the sample mean of iid rv's is known to be equivalent to the asymptotic normality condition (ANC) of Levy. And Levy's ANC is well known to be equivalent to an alternative ANC of Feller. Both are equivalent to a negligibility requirement, considered by O'Brien. More recently, additional equivalences have been developed in terms of the quantile function, by Cso...
متن کاملThe Martingale Central Limit Theorem
One of the most useful generalizations of the central limit theorem is the martingale central limit theorem of Paul Lévy. Lévy was in part inspired by Lindeberg’s treatment of the central limit theorem for sums of independent – but not necessarily identically distributed – random variables. Lindeberg formulated what, in retrospect, is the right hypothesis, now known as the Lindeberg condition,1...
متن کاملA Martingale Central Limit Theorem
We present a proof of a martingale central limit theorem (Theorem 2) due to McLeish (1974). Then, an application to Markov chains is given.
متن کاملChapter 5: Asymptotic Methods and Functional Central Limit Theorems
This chapter sketches the fundamentals of asymptotic distribution theory, and applies these speci cally to questions relating to weak convergence on function spaces. These results have important applications in the analysis of nonstationary time series models. A simple case of the functional central limit theorem for processes with independent increments is stated and proved, after detailing th...
متن کاملNotes on the Martingale Approach to Central Limit Theorems for Markov Chains
Notes on the Maxwell-Woodroofe martingale approach to central limit theorems for Markov chains.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1978
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700008169