Standard Deviation of the Mean of Autocorrelated Observations Estimated with the Use of the Autocorrelation Function Estimated From the Data

• Autorzy: Zięba A. , Ramza P.
• Języki publikacji: EN

Abstrakty

EN

Prior knowledge of the autocorrelation function (ACF) enables an application of analytical formalism for the unbiased estimators of variance s²a and variance of the mean s²a(x‾). Both can be expressed with the use of so-called effective number of observations neff. We show how to adopt this formalism if only an estimate {rk} of the ACF derived from a sample is available. A novel method is introduced based on truncation of the {rk} function at the point of its first transit through zero (FTZ). It can be applied to non-negative ACFs with a correlation range smaller than the sample size. Contrary to the other methods described in literature, the FTZ method assures the finite range 1 < nˆeff ≤ n for any data. The effect of replacement of the standard estimator of the ACF by three alternative estimators is also investigated. Monte Carlo simulations, concerning the bias and dispersion of resulting estimators sa and sa(x‾), suggest that the presented formalism can be effectively used to determine a measurement uncertainty. The described method is illustrated with the exemplary analysis of autocorrelated variations of the intensity of an X-ray beam diffracted from a powder sample, known as the particle statistics effect.

Słowa kluczowe

EN

autocorrelated data; time series; effective number of observations; estimators of variance; measurement uncertainty

• Wydawca: Komitet Metrologii i Aparatury Naukowej PAN
• Czasopismo: Metrology and Measurement Systems
• Rocznik: 2011
• Tom: Vol. 18, nr 4
• Strony: 529--542
• Opis fizyczny: Bibliogr. 12 poz., rys., tab., wykr.

Twórcy

autor

Zięba A.

autor

Ramza P.

• Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, Mickiewicza 30, 30-059 Krakow, Poland,

Bibliografia

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• [6] Zhang, N. F. (2006). Calculation of the uncertainty of the mean of autocorrelated measurements. Metrology, 43, 276-281.
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• [8] Quenouille, M. H. (1949). Approximate tests of correlation in time-series. J. R. Statist. Soc. B, 11, 68-84.
• [9] Marriott, F. H. C. Pope, J. A. (1954). Bias in the estimation of autocorrelations. Biometrika, 41, 390-402.
• [10] Zieba, A., Ramza, P., to be published.
• [11] ISO/IEC. (1995). Guide to the Expression of Uncertainty in Measurement. Geneva: ISO.
• [12] Dinnebier, R. E., Billinge, S. J. L. Eds. (2008). Powder Diffraction: Theory and Practice. Cambridge: RSC Publishing.