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Peakedness of linear forms in ensembles and mixtures

Listed author(s):
  • Jensen, D. R.
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    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.

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    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 35 (1997)
    Issue (Month): 3 (October)
    Pages: 277-282

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    Handle: RePEc:eee:stapro:v:35:y:1997:i:3:p:277-282
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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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