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A Monotonicity of Moments Concerned with Order Restricted Statistical Inference

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Abstract

In the order restricted statistical inference problem, moments of the distance between a true parameter and the least square estimate are non-decreasing when the true parameter moves along a half line from an initial point in the null space. This follows from “stochastically larger” property of the distance.

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References

  • Anraku, K. (1999). An information criterion for parameters under a simple order restriction, Biometrika, 86, 141–152.

    Google Scholar 

  • Barlow, R. E., Bartholomew, D. J., Bremner, J. M. and Brunk, H. D. (1972). Statistical Inference under Order Restrictions, Wiley, London.

    Google Scholar 

  • Mukerjee, H., Robertson, T. and Wright, F. T. (1986). A probability inequality for elliptically contoured densities with applications in order restricted inference, Ann. Statist., 14, 1548–1554.

    Google Scholar 

  • Nomakuchi, K. (1983). The likelihood ratio test of normal mean with hypothesis determined by a convex polyhedral cone and the monotonicity of its power function, Mem. Fac. Sci. Kyushu Univ. Ser. A, 37, 195–209.

    Google Scholar 

  • Perlman, M. D. (1969). One-sided problems in multivariate analysis, Ann. Math. Statist., 40, 549–567.

    Google Scholar 

  • Robertson, T., Wright, F. T. and Dykstra, R. L. (1988). Order Restricted Statistical Inference, Wiley, Chichester.

    Google Scholar 

  • Rockafellar, R. T. (1970). Convex Analysis, Princeton University Press, New Jersey.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and Information Science, Kochi University, Kochi, 780-8520, Japan

    Kentaro Nomakuchi

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  1. Kentaro Nomakuchi
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Nomakuchi, K. A Monotonicity of Moments Concerned with Order Restricted Statistical Inference. Annals of the Institute of Statistical Mathematics 54, 621–625 (2002). https://doi.org/10.1023/A:1022471313041

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  • DOI: https://doi.org/10.1023/A:1022471313041

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