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Modeling annual rainfall: a robust maximum likelihood approach
Author(s) -
Haddad John N.,
Nimah Musa N.,
Farajallah Nadim
Publication year - 2007
Publication title -
environmetrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.68
H-Index - 58
eISSN - 1099-095X
pISSN - 1180-4009
DOI - 10.1002/env.805
Subject(s) - autoregressive model , mathematics , estimator , maximum likelihood , statistics , likelihood function , realization (probability) , restricted maximum likelihood , zero (linguistics) , gaussian , interval (graph theory) , function (biology) , transformation (genetics) , combinatorics , physics , biochemistry , chemistry , quantum mechanics , evolutionary biology , gene , biology , linguistics , philosophy
Let { X t } be a zero mean, Gaussian, autoregressive process of order one with parameter α. For a realization (X 1 ,X 2 ,…,X n )′ of { X t }, we consider the transformation Y t = X t /X t−1 , for t = 2,…, n. Then the likelihood function of (Y 2 ,…, Y n ) can be derived and is shown to be independent of the parameter σ 2 . Now, maximum likelihood estimator for α is derived and interval estimates are then computed and used to determine the influence of each data point. Finally, a direct application to precipitation data will be given for illustration. Copyright © 2006 John Wiley & Sons, Ltd.
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