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Revisiting Best Linear Unbiased Estimation of Location-Scale Parameters Based on Optimally Selected Order Statistics Using Compound Design

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  • Narayanaswamy Balakrishnan

    (McMaster University)

  • Ritwik Bhattacharya

    (School of Engineering and Sciences, Tecnológico de Monterrey)

Abstract

We introduce here the compound optimal design strategy to determine the Best Linear Unbiased Estimates (BLUEs) of location and scale parameters based on suitably chosen few order statistics. It is shown that the linear estimates of the parameters from any location-scale distribution, based on few optimally chosen ranks, obtained from the compound optimal design criterion is indeed the BLUE. Further extension of the strategy to Asymptotically Best Linear Unbiased Estimates (ABLUEs) is also discussed. The validation of the proposed strategy is justified through a numerical study for normal, Laplace and logistic distributions. Finally, a real-life data set is analyzed to illustrate the proposed strategy.

Suggested Citation

  • Narayanaswamy Balakrishnan & Ritwik Bhattacharya, 2022. "Revisiting Best Linear Unbiased Estimation of Location-Scale Parameters Based on Optimally Selected Order Statistics Using Compound Design," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1891-1915, September.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:3:d:10.1007_s11009-021-09891-5
    DOI: 10.1007/s11009-021-09891-5
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    References listed on IDEAS

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    1. N. Balakrishnan & Z. Govindarajulu & K. Balasubramanian, 1993. "Relationships between moments of two related sets of order statistics and some extensions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(2), pages 243-247, June.
    2. Lorens Imhof & Weng Kee Wong, 2000. "A Graphical Method for Finding Maximin Efficiency Designs," Biometrics, The International Biometric Society, vol. 56(1), pages 113-117, March.
    3. Ritwik Bhattacharya, 2020. "Implementation of compound optimal design strategy in censored life-testing experiment," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 1029-1050, December.
    4. Ritwik Bhattacharya & Baidya Nath Saha & Graceila González Farías & Narayanaswamy Balakrishnan, 2020. "Multi-criteria-based optimal life-testing plans under hybrid censoring scheme," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(2), pages 430-453, June.
    Full references (including those not matched with items on IDEAS)

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