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Improved estimation of medians subject to order restrictions in unimodal symmetric families

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  • Garren Steven T.

Abstract

Suppose mutually independent observations are drawn from absolutely continuous, unimodal, symmetric distributions with an order restriction on the medians, μ0 ≤ min{μ1,μ2,...,μm}. An isotonic regression estimator is shown to stochastically dominate the marginal sample median when estimating μ0, under some regularity conditions. These conditions allow the tails of the first population (i.e., the population with median μ0) to be quite heavy, whereas the tails of the remaining distributions are required to be relatively light. Examples involving the Cauchy and Laplace distributions are shown to satisfy these regularity conditions. Counterexamples illustrate the importance of these regularity conditions for proving stochastic domination. The results expressed herein are theoretical advancements in order restricted inference.

Suggested Citation

  • Garren Steven T., 2003. "Improved estimation of medians subject to order restrictions in unimodal symmetric families," Statistics & Risk Modeling, De Gruyter, vol. 21(4), pages 367-380, April.
    • Handle: RePEc:bpj:strimo:v:21:y:2003:i:4/2003:p:367-380:n:5
    DOI: 10.1524/stnd.21.4.367.25347
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    References listed on IDEAS

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    6. Rueda, C. & Salvador, B. & Fernández, M. A., 1997. "Simultaneous Estimation in a Restricted Linear Model," Journal of Multivariate Analysis, Elsevier, vol. 61(1), pages 61-66, April.
    7. Misra, Neeraj & van der Meulen, Edward C., 1997. "On estimation of the common mean of k ([greater-or-equal, slanted] 2) normal populations with order restricted variances," Statistics & Probability Letters, Elsevier, vol. 36(3), pages 261-267, December.
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