Variance stabilizing transformation and studentization for estimator of correlation coefficient

Fujisawa, Hironori

doi:10.1016/s0167-7152(99)00158-3

Cited by 3 publications

(2 citation statements)

References 16 publications

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“…Folklore backed by many simulation studies indicates, however, that the variance stabilized statistic has better small sample properties. For a result backing this belief, based on an asymptotic expansion of the distributions, see Fujisawa (2000).…”

Section: Introductionmentioning

confidence: 98%

Advantages of Variance Stabilization

Morgenthaler

Staudte

2012

Scandinavian J Statistics

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Variance stabilization is a simple device for normalizing a statistic. Even though its large sample properties are similar to those of studentizing, many simulation studies of confidence interval procedures show that variance stabilization works better for small samples. We investigated this question in the context of testing a null hypothesis involving a single parameter. We provide support for a measure of evidence for an alternative hypothesis that is simple to compute, calibrate and interpret. It has applications in most routine problems in statistics, and leads to more accurate confidence intervals, estimated power and hence sample size calculations than standard asymptotic methods. Such evidence is readily combined when obtained from different studies. Connections to other approaches to statistical evidence are described, with a notable link to Kullback-Leibler symmetrized divergence.

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Section: Introductionmentioning

confidence: 98%

Advantages of Variance Stabilization

Morgenthaler

Staudte

2012

Scandinavian J Statistics

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“…Then r n = T n /S n is the sample correlation coefficient. Fujisawa (2000) discussed the normalizing transformation of the coefficient r n . He obtained the transformation when the underlying distributions are a bivariate normal and an elliptical distribution.…”

Section: Correlation Coefficientmentioning

confidence: 99%

Edgeworth Expansion and Normalizing Transformation of Ratio Statistics and Their Application

Maesono

2010

Communications in Statistics - Theory and Methods

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Some statistics in common use take a form of a ratio of two statistics, such as sample correlation coefficient, Pearson's coefficient of variation, cumulant estimators and so on. In this paper, using an asymptotic representation of the ratio statistics, we will obtain an Edgeworth expansion and a normalizing transformation with remainder term o(n −1/2). The Edgeworth expansion is based on a studentized ratio statistic, which is studentized by a consistent variance estimator. Applying these results to the sample correlation coefficient, we obtain the normalizing transformation and an asymptotic confidence interval of the correlation coefficient without assuming specific underlying distribution. This normalizing transformation is an extension of the Fisher's z-transformation.

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