Maximizing the probability of correctly ordering random variables using linear predictors

Stephen Portnoy

Journal of Multivariate Analysis, 1982, vol. 12, issue 2, 256-269

Abstract: Let (T1, x1), (T2, x2), ..., (Tn, xn) be a sample from a multivariate normal distribution where Ti are (unobservable) random variables and xi are random vectors in Rk. If the sample is either independent and identically distributed or satisfies a multivariate components of variance model, then the probability of correctly ordering {Ti} is maximized by ranking according to the order of the best linear predictors {E(Tixi)}. Furthermore, it orderings are chosen according to linear functions {b'xi} then the conditional probability of correct order given (Ti = t1; I = 1, ..., n) is maximized when b'xi is the best linear predictor. Examples are given to show that linear predictors may not be optimal and that using a linear combination other that the best linear predictor may give a greater probability of correctly ordering {Ti} if {(Ti, xi)} are independent but not identically distributed, or if the distributions are not normal.

Keywords: Linear; predictors; selection; index; multivariate; normal (search for similar items in EconPapers)
Date: 1982
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Citations: View citations in EconPapers (2)

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