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FINITE-SAMPLE MOMENTS OF THE COEFFICIENT OF VARIATION

Published online by Cambridge University Press:  01 February 2009

Yong Bao
Yong Bao*
Affiliation:
Purdue University
*
*Address correspondence to Yong Bao, Department of Economics, Purdue University, 403 W. State St., West Lafayette, IN 47907, USA; e-mail: ybao@purdue.edu.
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Abstract

We study the finite-sample bias and mean squared error, when properly defined, of the sample coefficient of variation under a general distribution. We employ a Nagar-type expansion and use moments of quadratic forms to derive the results. We find that the approximate bias depends on not only the skewness but also the kurtosis of the distribution, whereas the approximate mean squared error depends on the cumulants up to order 6.

Type
NOTES AND PROBLEMS
Information
Econometric Theory , Volume 25 , Issue 1 , February 2009 , pp. 291 - 297
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Bao, Y. & Ullah, A. (2007) Expectation of Quadratic Forms in Normal and Nonnormal Variables with Econometric Applications. Manuscript, Temple University.Google Scholar
Baumol, W. & Wolff, E.N. (1988) Productivity growth, convergence, and welfare: Reply. American Economic Review 78, 1155–1159.Google Scholar
Breunig, R. (2001) An almost unbiased estimator of the coefficient of variation. Economics Letters 70, 15–19.CrossRefGoogle Scholar
Coughlin, C.C., Garrett, T.A., & Hernández-Murillo, R. (2007) Spatial dependence in models of state fiscal policy convergence. Public Finance Review 35, 361–384.CrossRefGoogle Scholar
Dalgaard, C.-J. & Vastrup, J. (2001) On the measurement of σ-convergence. Economics Letters 70, 283–287.CrossRefGoogle Scholar
Fisher, R.A. (1928) Moments and product moments of sampling distributions. Proceedings of the London Mathematical Society 30, 199–238.Google Scholar
Giannias, D., Liargovas, P., & Manolas, G. (1999) Quality of life indices for analysing convergence in the European Union. Regional Studies 33, 27–35.CrossRefGoogle Scholar
Helliwell, J.F. (1996) Convergence and migration among provinces. Canadian Journal of Economics 29, 324–330.CrossRefGoogle ScholarPubMed
Kendall, M. & Stuart, A. (1977) The Advanced Theory of Statistics, 4th ed.Charles Griffin.Google Scholar
Lieberman, O. (1994) A Laplace approximation to the moments of a ratio of quadratic forms. Biometrika 81, 681–690.CrossRefGoogle Scholar
Nagar, A.L. (1959) The bias and moment matrix of the general k-class estimators of the parameters in simultaneous equations. Econometrica 27, 575–595.CrossRefGoogle Scholar
Ravallion, M. (1994) Poverty Comparisons. Harwood Academic.Google Scholar
Rilstone, P., Srivastava, V.K., & Ullah, A. (1996) The second-order bias and mean squared error of nonlinear estimators. Journal of Econometrics 75, 369–395.CrossRefGoogle Scholar
Roberts, L.A. (1992) On ratios of random variables and generalised mortality rates. Journal of Applied Probability 29, 268–279.CrossRefGoogle Scholar
Roberts, L.A. (1995) On the existence of moments of ratios of quadratic forms. Econometric Theory 11, 750–774.CrossRefGoogle Scholar
Ullah, A. & Srivastava, V.K. (1994) Moments of the ratio of quadratic forms in non-normal variables with econometric examples. Journal of Econometrics 62, 129–141.CrossRefGoogle Scholar
Ullah, A., Srivastava, V.K., & Roy, N. (1995) Moments of the function of non-normal random vector with applications to econometric estimators and test statistics. Econometric Reviews 14, 459–471.CrossRefGoogle Scholar