Some applications of inequalities for extreme order statistics to a genetic selection problem.
Two inequalities are derived for the extreme order statistics in a special case of unequally-correlated multivariate normal variables, and their implications in a genetic selection problem which was considered recently by Rawlings (1976, Biometrics 32, 875-887) and Hill (1976, Biometrics 32, 889-902; 1977, Biometrics 33, 703-712) are discussed. The inequalities establish a monotonicity property of the extreme order statistics as a function of the intraclass correlation, and they yield a chain of bounds when the family sizes are not all equal. Thus the inequalities extend the applicability of the results given by Rawlings and Hill to the more general case.
D000818:Animals; D008433:Mathematics; D008957:Models, Genetic; D011336:Probability; D012641:Selection, Genetic; D013223:Statistics as Topic