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The use of spacings in the estimation of a scale parameter

Author

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  • Balakrishnan, N.
  • Papadatos, N.

Abstract

Linear functions on spacings--instead of linear functions on order statistics--are considered, in order to simplify the form of best linear unbiased estimators (BLUEs) and best linear invariant estimators (BLIEs) for the scale parameter in the classical location-scale family. Also, a sufficient condition for the non-negativity of the scale estimator is presented and, moreover, necessary and sufficient conditions for the BLUE (and the BLIE) to be a constant multiple of the sample range are derived. Finally, a modification of this approach is applied in order to simplify the derivations of both the location and the scale estimators in the Uniform Type-II Censored model.

Suggested Citation

  • Balakrishnan, N. & Papadatos, N., 2002. "The use of spacings in the estimation of a scale parameter," Statistics & Probability Letters, Elsevier, vol. 57(2), pages 193-204, April.
    • Handle: RePEc:eee:stapro:v:57:y:2002:i:2:p:193-204
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    References listed on IDEAS

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    1. Bai, Zhidong & Sarkar, Sanat K. & Wang, Wenjin, 1997. "Positivity of the best unbiased L-estimator of the scale parameter with complete or selected order statistics from location-scale distribution," Statistics & Probability Letters, Elsevier, vol. 32(2), pages 181-188, March.
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    Cited by:

    1. Nickos Papadatos, 2012. "Linear estimation of location and scale parameters using partial maxima," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(2), pages 243-270, February.
    2. Burkschat, M., 2009. "Multivariate dependence of spacings of generalized order statistics," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1093-1106, July.
    3. Chen, Huaihou & Xie, Hongmei & Hu, Taizhong, 2009. "Log-concavity of generalized order statistics," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 396-399, February.

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    1. Burkschat, M., 2009. "Multivariate dependence of spacings of generalized order statistics," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1093-1106, July.
    2. Nickos Papadatos, 2012. "Linear estimation of location and scale parameters using partial maxima," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(2), pages 243-270, February.

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