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Why your model parameter confidences might be too optimistic. Unbiased estimation of the inverse covariance matrix

J. HartlapArgelander-Institut (Founded by merging of the Sternwarte, Radioastronomisches Institut and Institut für Astrophysik und Extraterrestrische Forschung der Universität Bonn.) für Astronomie, Universität Bonn, Auf dem Hügel 71, 53121 Bonn, Germany e-mail: [email protected]P. ŠimonArgelander-Institut (Founded by merging of the Sternwarte, Radioastronomisches Institut and Institut für Astrophysik und Extraterrestrische Forschung der Universität Bonn.) für Astronomie, Universität Bonn, Auf dem Hügel 71, 53121 Bonn, Germany e-mail: [email protected]Peter SchneiderArgelander-Institut (Founded by merging of the Sternwarte, Radioastronomisches Institut and Institut für Astrophysik und Extraterrestrische Forschung der Universität Bonn.) für Astronomie, Universität Bonn, Auf dem Hügel 71, 53121 Bonn, Germany e-mail: [email protected]
2006en
ABI

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Aims.The maximum-likelihood method is the standard approach to obtain model fits to observational data and the corresponding confidence regions. We investigate possible sources of bias in the log-likelihood function and its subsequent analysis, focusing on estimators of the inverse covariance matrix. Furthermore, we study under which circumstances the estimated covariance matrix is invertible.

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