Peakedness of linear forms in ensembles and mixtures

D. R. Jensen

Statistics & Probability Letters, 1997, vol. 35, issue 3, 277-282

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.

Keywords: Estimating; location; Weighted; averages; Concentration; Majorization; Star-contoured; distributions; Monotone; consistency (search for similar items in EconPapers)
Date: 1997
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Citations: View citations in EconPapers (5)

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