Climatic Indices, Principal Components, and the Gauss-Markov Theorem

Autor:	R. Lewandowicz, W. C. Thacker
Rok vydání:	1996
Předmět:	Atmospheric Science Covariance matrix Climatology Singular value decomposition Principal component analysis Calculus Applied mathematics Statistical model Linear combination Canonical correlation Eigenvalues and eigenvectors Gauss–Markov theorem Mathematics
Zdroj:	Journal of Climate. 9:1942-1958
ISSN:	1520-0442 0894-8755
Popis:	If indices are to be used as the variables predicted by linear statistical models, it is important to be able to recover as much local information as possible from the values forecast for the indices. Here it is shown that the indices that encapsulate the most information about the local climatic state are determined by a generalized (two-matrix) eigenvalue problem that is equivalent to the usual (one-matrix) eigenvalue problem involving the sample correlation matrix. Thus, the best indices in the sense of providing the most location-specific information are familiar principal-component indices. Regarding the indices as predictors in linear statistical models similar to those routinely used for estimating meteorological fields from observations reveals the role of the Gauss-Markov theorem in EOF analyses. From this perspective each index can he characterized by two EOF-like maps: the first illustrating the linear combinations of the data used to define the index, and the second displaying the Gau...
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::24fc2c865afab445285bbd6fd5de79e6 https://doi.org/10.1175/1520-0442(1996)009<1942:cipcat>2.0.co Zobrazit plný text záznamu