Estimates of low bias for the multivariate normal
Given a sample from a multivariate normal with mean , a method is given for obtaining estimates with low bias for a function of the parameters. When the function is a product of positive powers of the parameters, an unbiased estimate is available. Estimates of ratios like [mu]1/[mu]2 are given with bias ~n-5, where n is the sample size. Simulation studies show superior performance of these estimates versus traditional ones.
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Volume (Year): 81 (2011)
Issue (Month): 11 (November)
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References listed on IDEAS
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- Dongchu Sun & Xiaoqian Sun, 2005. "Estimation of the multivariate normal precision and covariance matrices in a star-shape model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(3), pages 455-484, September.
- Yanagihara, Hirokazu, 2006. "Corrected version of AIC for selecting multivariate normal linear regression models in a general nonnormal case," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1070-1089, May.
- Misra, Neeraj & Singh, Harshinder & Demchuk, Eugene, 2005. "Estimation of the entropy of a multivariate normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 92(2), pages 324-342, February.
- Kollo, T. & Vonrosen, D., 1995. "Minimal Moments and Cumulants of Symmetric Matrices: An Application to the Wishart Distribution," Journal of Multivariate Analysis, Elsevier, vol. 55(2), pages 149-164, November.
- Sun, Dongchu & Sun, Xiaoqian, 2006. "Estimation of multivariate normal covariance and precision matrices in a star-shape model with missing data," Journal of Multivariate Analysis, Elsevier, vol. 97(3), pages 698-719, March.
- Zografos, K. & Nadarajah, S., 2005. "Expressions for Rényi and Shannon entropies for multivariate distributions," Statistics & Probability Letters, Elsevier, vol. 71(1), pages 71-84, January.
- Hutson, Alan D., 2002. "Quasi-medians are robust and relatively efficient estimators of a common mean given multivariate normality," Statistics & Probability Letters, Elsevier, vol. 57(4), pages 403-408, May.
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