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Peakedness of linear forms in ensembles and mixtures

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  • Jensen, D. R.

Abstract

Linear forms are studied in random variables {X1, ... , Xn} having common location-scale parameters ([mu], [sigma]2). For certain distributions on Rn having star-shaped contours and others, it is shown that if q = [q1, ... , qn]' majorizes p = [p1, ... , pn]', then is more peaked about [mu] than than W(q) in the sense of Birnbaum (1948). In particular, the peakedness about [mu] of increases monotonically with n. If neither c nor d majorizes the other, then {W (c), W (d)} are less peaked about [mu] than W (c [logical and] d), and are more peaked than W (c [logical or] d). This extends the findings of Proschan (1965) and Olkin and Tong (1988). Stochastic majorants and minorants for linear estimators are given in certain ensembles, including star-contoured distributions on Rn if ordered by peakedness.

Suggested Citation

  • Jensen, D. R., 1997. "Peakedness of linear forms in ensembles and mixtures," Statistics & Probability Letters, Elsevier, vol. 35(3), pages 277-282, October.
  • Handle: RePEc:eee:stapro:v:35:y:1997:i:3:p:277-282
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    References listed on IDEAS

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    1. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
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    Cited by:

    1. Rustam Ibragimov, 2005. "Portfolio Diversification and Value At Risk Under Thick-Tailedness," Yale School of Management Working Papers amz2386, Yale School of Management, revised 01 Aug 2005.
    2. Rustam Ibragimov, 2004. "Shifting paradigms: on the robustness of economic models to heavy-tailedness assumptions," Econometric Society 2004 Latin American Meetings 105, Econometric Society.
    3. Ibragimov, Rustam, 2007. "Efficiency of linear estimators under heavy-tailedness: convolutions of [alpha]-symmetric distributions," Scholarly Articles 2623749, Harvard University Department of Economics.
    4. Jensen, D. R., 2003. "On the monotone convergence of vector means," Journal of Multivariate Analysis, Elsevier, vol. 85(1), pages 78-90, April.
    5. Rustam Ibragimov, 2005. "Portfolio Diversification and Value At Risk Under Thick-Tailedness," Yale School of Management Working Papers amz2386, Yale School of Management, revised 01 Aug 2005.

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