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THE EFFECTS OF CORRELATION AMONG OBSERVATIONS ON THE ACCURACY OF APPROXIMATING THE DISTRIBUTION OF SAMPLE MEAN BY ITS ASYMPTOTIC DISTRIBUTION 1
Author(s) -
Sharma Subhash C.
Publication year - 1985
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1985.tb00556.x
Subject(s) - mathematics , correlation , sample size determination , statistics , distribution (mathematics) , upper and lower bounds , sample (material) , distribution function , mathematical analysis , physics , geometry , quantum mechanics , thermodynamics
Summary In this paper, we investigate the effects of correlation among observations on the accuracy of approximating the distribution of sample mean by its asymptotic distribution. The accuracy is investigated by the Berry‐Esseen bound (BEB), which gives an upper bound on the error of approximation of the distribution function of the sample mean from its asymptotic distribution for independent observations. For a given sample size (n 0 ) the BEB is obtained when the observations are independent. Let this be BEB. We then find the sample size (n * ) required to have BEB below BEB 0 , when the observations are dependent. Comparison of n * with n 0 reveals the effects of correlation among observations on the accuracy of the asymptotic distribution as an approximation. It is shown that the effects of correlation among observations are not appreciable if the correlation is moderate to small but it can be severe for extreme correlations.