Document Zbl 0489.62050

Some finite sample results for the selection differential. (English) Zbl 0489.62050

Ann. Inst. Stat. Math. 33, 437-448 (1981).

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MSC:

62G30	Order statistics; empirical distribution functions
62E15	Exact distribution theory in statistics

Keywords:

order statistics; selection differential; bounds on expectations; finite sample results; Cauchy-Schwarz technique; convex transformations

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References:

[1]	Arnold, B. C. and Groeneveld, R. A. (1979). Bounds on expectations of linear systematic statistics based on dependent samples,Ann. Statist.,7, 220-223. · Zbl 0398.62036 · doi:10.1214/aos/1176344567
[2]	David, H. A. (1981).Order Statistics, 2nd ed., John Wiley & Sons, Inc., New York. · Zbl 0553.62046
[3]	Falconer, D. S. (1960).Introduction to Quantitative Genetics, The Ronald Press Co., New York.
[4]	Feller, W. (1966).An Introduction to Probability Theory and its Applications, Vol. II, John Wiley & Sons, Inc., New York. · Zbl 0138.10207
[5]	Mallows, C. L. and Richter, D. (1969). Inequalities of Chebychev type involving conditional expectations,Ann. Math. Statist.,40, 1922-1932. · Zbl 0187.14903 · doi:10.1214/aoms/1177697276
[6]	Teichroew, D. (1956). Tables of expected values of order statistics and products of order statistics for samples of size 20 and less from the normal distribution.Ann. Math. Statist.,27, 410-426. · Zbl 0071.13501 · doi:10.1214/aoms/1177728266
[7]	van Zwet, W. R. (1964).Convex Transformations of Random Variables, Mathematical Centre Tracts 7 Mathematisch Centrum, Amsterdam. · Zbl 0125.37102

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