Mai, M. Hugo (2024) Estimation of generalized cumulants and their generalization PRE - Research Project, ENSTA.
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Abstract
In a first phase, the project consists in rewriting in Python the R library kStatistics package., which provides estimators (kstatistics) of cumulants (univariate and multivariate) and cumulant products (polykays, univariate and multivariate). For the contents of the package refer to the paper (2022) Di Nardo E., Guarino G. kStatistics: Unbiased Estimates of Joint Cumulant Products from the Multivariate Faà Di Bruno’s Formula. The R Journal. 14(2) 208-228. In a second phase the aim is to construct routines for generating generalized cumulants in Phyton. Generalized cumulants make use of complementary set partitions that are difficult to implement and involve cumulants according to special grouping rules There are tables in Prof. McCullagh’s (Univ. Chicago) book. The idea is to study and propose an easy-to-implement algorithm for generating these indexes. Moreover, using multivariate polykays, proper estimators can be constructed. A final goal is to study and implement algorithms for constructing cumulants of the polykays and their estimators (always in Python)
Item Type: | Thesis (PRE - Research Project) |
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Uncontrolled Keywords: | kstatistics, programming, estimators |
Subjects: | Mathematics and Applications |
ID Code: | 10254 |
Deposited By: | Hugo MAI |
Deposited On: | 09 sept. 2024 10:53 |
Dernière modification: | 09 sept. 2024 10:53 |
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