References

ESTIMATING A STANDARD DEVIATION WITH U-STATISTICS OF DEGREE MORE THAN TWO: THE NORMAL CASE


[1] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, Dover, New York, 1972.

[2] B. C. Arnold, Majorization and the Lorenz Order: A Brief Introduction, Lecture Notes in Statistics, Springer-Verlag, New York, 1987.

[3] B. C. Arnold, Inequality measures for multivariate distributions, Metron 3 (2005), 317-327.

[4] Ralph B. D’Agostino, Linear estimation of the normal distribution standard deviation, American Statistician 24 (1970), 14-15.

[5] F. Downton, Linear estimates with polynomial co-efficients, Biometrika 53 (1966), 129-141.

[6] M. Ghosh, N. Mukhopadhyay and P. K. Sen, Sequential Estimation, Wiley, New York, 1997.

[7] C. Gini, L’Ammontare la Composizione della Ricchezza delle Nazioni, Torino, Boca Raton, 1914.

[8] C. Gini, Measurement of inequality of incomes, Economic Journal 31 (1921), 124-126.

[9] T. P. Hettmansperger and J. W. McKean, Robust Nonparametric Statistical Methods, Arnold, London, 1998.

[10] W. Hoeffding, A class of statistics with asymptotically normal distribution, Ann. Math. Stat. 19 (1948), 293-325.

[11] W. Hoeffding, The Strong Law of Large Numbers for U-Statistics, Institute of Statistics Mimeo Series, No. 302, University of North Carolina, Chapel Hill, North Carolina, 1961.

[12] M. Hollander and D. A. Wolfe, Nonparametric Statistical Methods, Second Edition, Wiley, New York, 1999.

[13] J. Jureckova and P. K. Sen, Robust Statistical Procedures: Asymptotics and Interrelations, Wiley, New York, 1996.

[14] V. S. Korolyuk and Yu. V. Borovskich, Theory of U-Statistics, Springer, Netherland, 2009.

[15] J. Kowalski and X. M. Tu, Modern Applied U-Statistics, Wiley, New York, 2007.

[16] A. J. Lee, U-Statistics, CRC, Boca Raton, 1990.

[17] N. Mukhopadhyay and T. K. S. Solanky, Multistage Selection and Ranking Procedures: Second-Order Asymptotics, Dekker, New York, 1994.

[18] N. Mukhopadhyay and B. Chattopadhyay, Revisiting Sample Variance with Alternative Constructions, Department of Statistics Tech. Rep. No. 10-47, University of Connecticut, Storrs, Connecticut, 2010.

[19] U. S. Nair, The standard error of Gini’s mean difference, Biometrika 28 (1936), 428-436.

[20] M. L. Puri and P. K. Sen, Nonparametric Methods in Multivariate Analysis, Wiley, New York, 1971.

[21] P. K. Sen, Sequential Nonparametrics: Invariance Principles and Statistical Inference, Wiley, New York, 1981.

[22] P. K. Sen, The Gini coefficient and poverty indexes: Some reconciliations, J. Amer. Stat. Assoc. 81 (1986), 1050-1057.

[23] Amartya Sen, On Economic Inequality (Expanded edition with a substantial annexe by J. E. Foster and A. Sen), Clarendon Press, Oxford, 1997.

[24] S. Yitzhaki, Gini’s mean difference: A superior measure of variability for non- normal distribution, Metron 61 (2003), 285-316.