An almost unbiased estimator of the coefficient of variation

Breunig, Robert

doi:10.1016/s0165-1765(00)00351-7

Cited by 61 publications

(44 citation statements)

References 4 publications

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“…Breunig [10] examined the distribution of δ 2 . He derived expressions for the bias of δ 2 up to order N −1 and for the mean square error of δ 2 up to order N −2 .…”

Section: Existing Univariate Resultsmentioning

confidence: 99%

“…and p * is defined in (10). The estimator in (13) is a minor variation of an estimator proposed by Yuan and Bentler [60].…”

Section: New Multivariate Resultsmentioning

confidence: 99%

“…where D p and p * are defined in (10) and N p is defined in (12). Estimators of and λ are obtained as minimizers of SSE(θ ) with respect to θ , where , where is defined in (15) and (16).…”

Section: Principal Component Models For the CV Matrixmentioning

confidence: 99%

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Principal components on coefficient of variation matrices

Boik

Shirvani

2009

Statistical Methodology

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“…Breunig [10] examined the distribution of δ 2 . He derived expressions for the bias of δ 2 up to order N −1 and for the mean square error of δ 2 up to order N −2 .…”

Section: Existing Univariate Resultsmentioning

confidence: 99%

“…and p * is defined in (10). The estimator in (13) is a minor variation of an estimator proposed by Yuan and Bentler [60].…”

Section: New Multivariate Resultsmentioning

confidence: 99%

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Principal components on coefficient of variation matrices

Boik

Shirvani

2009

Statistical Methodology

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“…We do not consider the case of a nonexisting second moment (Segev et al, 2002). Breunig (2001) gives the bias of CV 2 :…”

Section: Single Samplementioning

confidence: 99%

Firing Variability Is Higher than Deduced from the Empirical Coefficient of Variation

Ditlevsen

Lánský

2011

Neural Computation

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A convenient and often used summary measure to quantify the firing variability in neurons is the coefficient of variation (CV), defined as the standard deviation divided by the mean. It is therefore important to find an estimator that gives reliable results from experimental data, that is, the estimator should be unbiased and have low estimation variance. When the CV is evaluated in the standard way (empirical standard deviation of interspike intervals divided by their average), then the estimator is biased, underestimating the true CV, especially if the distribution of the interspike intervals is positively skewed. Moreover, the estimator has a large variance for commonly used distributions. The aim of this letter is to quantify the bias and propose alternative estimation methods. If the distribution is assumed known or can be determined from data, parametric estimators are proposed, which not only remove the bias but also decrease the estimation errors. If no distribution is assumed and the data are very positively skewed, we propose to correct the standard estimator. When defining the corrected estimator, we simply use that it is more stable to work on the log scale for positively skewed distributions. The estimators are evaluated through simulations and applied to experimental data from olfactory receptor neurons in rats.

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“…See Kakwani (1980) or Ravallion (1994) for a review of income inequality estimation. Breunig (2001) discusses the bias problem and demonstrates how the large-n expansion may be used to derive a bias-corrected estimator. The purpose of this paper is to apply the bias correction technique developed in that paper for the coe cient of variation squared (CV 2 ) to income data from China and Kenya.…”

Section: Introductionmentioning

confidence: 99%

Bias correction for inequality measures: an application to China and Kenya

Breunig¹

2002

Applied Economics Letters

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An analytical bias correction technique for inequality measures is applied to income data from China and Kenya. The coefficient of variation squared is used and it is illustrated how the bias is downward for positively skewed distributions. The analytical bias correction technique is then compared to a jackknife estimator in a simulation exercise. The bias will be important, even for moderately large sample sizes.

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An almost unbiased estimator of the coefficient of variation

Cited by 61 publications

References 4 publications

Principal components on coefficient of variation matrices

Principal components on coefficient of variation matrices

Firing Variability Is Higher than Deduced from the Empirical Coefficient of Variation

Bias correction for inequality measures: an application to China and Kenya

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