Cornish-Fisher Expansions for Functionals of the Weighted Partial Sum Empirical Distribution

Autor: Saralees Nadarajah, Christopher S. Withers
Rok vydání: 2021
Předmět:
Zdroj: Methodology and Computing in Applied Probability. 24:1791-1804
ISSN: 1573-7713
1387-5841
Popis: Given a random sample X1,…,Xn in $\mathbb {R}^{p}$ from some distribution F and real weights w1, n,…,wn, n adding to n, define the weighted partial sum empirical distribution as $$ \begin{array}{@{}rcl@{}} \displaystyle G_{n} (\textbf{x}, t) = n^{-1} \sum\limits_{i=1}^{[nt]} w_{i, n} I \left( \textbf{X}_{i} \leq \textbf{x} \right) \end{array} $$ for x in $\mathbb {R}^{p}$ , 0 ≤ t ≤ 1. We give Cornish-Fisher expansions for smooth functionals of Gn, following up on Withers and Nadarajah (Statistical Methodology 12:1–15, 2013) who gave expansions for the unweighted version. Applications to sequential analysis include weighted cusum-type functionals for monitoring variance, and a Studentized weighted cusum-type functional for monitoring the mean.
Databáze: OpenAIRE
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