Effective number of observations and unbiased estimators of variance for autocorrelated data - an overview

• Autorzy: Zięba A.
• Języki publikacji: EN

Abstrakty

EN

When observations are autocorrelated, standard formulae for the estimators of variance, s², and variance of the mean, s²(x), are no longer adequate. They should be replaced by suitably defined estimators, sa² and sa²(x), which are unbiased given that the autocorrelation function is known. The formula for sa² was given by Bayley and Hammersley in 1946, this work provides its simple derivation. The quantity named effective number of observations neff is thoroughly discussed. It replaces the real number of observations n when describing the relationship between the variance and variance of the mean, and can be used to express sa² and sa²(x) in a simple manner. The dispersion of both estimators depends on another effective number called the effective degrees of freedom veff. Most of the formulae discussed in this paper are scattered throughout the literature and not very well known, this work aims to promote their more widespread use. The presented algorithms represent a natural extension of the GUM formulation of type-A uncertainty for the case of autocorrelated observations.

Słowa kluczowe

EN

autocorrelated; time series; estimator; unbiased; variance; effective number of observations

• Wydawca: Komitet Metrologii i Aparatury Naukowej PAN
• Czasopismo: Metrology and Measurement Systems
• Rocznik: 2010
• Tom: Vol. 17, nr 1
• Strony: 3--16
• Opis fizyczny: Bibliogr. 31 poz., wykr., wzory

Twórcy

autor

Zięba A.

• AGH University of Science and Technology, Department of Physics and Applied Computer Science, A. Mickiewicza 30, 30-059 Kraków, Poland,

Bibliografia

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