Asymptotic Normality Through Factorial Cumulants and Partition Identities
نویسندگان
چکیده
منابع مشابه
Asymptotic Normality Through Factorial Cumulants and Partition Identities
In the paper we develop an approach to asymptotic normality through factorial cumulants. Factorial cumulants arise in the same manner from factorial moments as do (ordinary) cumulants from (ordinary) moments. Another tool we exploit is a new identity for 'moments' of partitions of numbers. The general limiting result is then used to (re-)derive asymptotic normality for several models including ...
متن کاملCumulants and Bartlett Identities in Cox Regression
Expressions are found for the cumulants needed to analyze and improve the accuracy of Cox regression up to order O(n−3/2), and consistent estimators for these are given. In addition, the Bartlett identities are shown to hold for the Cox partial likelihood (and, in a broad sense, for partial likelihood in general), so that the cumulant estimators found can be used to adjust statistics in accorda...
متن کاملConsistency and Asymptotic Normality
The consistency and asymptotic normality of minimum contrast estimation (which includes the maximum likelihood estimation as a special case) is established if the sample is from a renewal process and the observation time tends to innnity. It is shown, that the conditions for consistency and asymptotic normality for maximum likelihood estimation are fulllled if the distribution of the time betwe...
متن کاملPartition Identities
A partition of a positive integer n (or a partition of weight n) is a non-decreasing sequence λ = (λ1, λ2, . . . , λk) of non-negative integers λi such that ∑k i=1 λi = n. The λi’s are the parts of the partition λ. Integer partitions are of particular interest in combinatorics, partly because many profound questions concerning integer partitions, solved and unsolved, are easily stated, but not ...
متن کاملAsymptotic expansions of moments and cumulants
Many parameters may be expanded as series with terms involving products of expectations and their estimates expanded as series involving products of averages. The computation of moments and cu-mulants of such estimates may be organized if the terms of the series expansions of parameters, estimates and their moments are considered as functions applied to lists. The lists form a vectors space ass...
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: Combinatorics, Probability and Computing
سال: 2012
ISSN: 0963-5483,1469-2163
DOI: 10.1017/s0963548312000545