Abstract
Let X={X(1),X(2),⃛, X(n)} a collection of real numbers, ordered from smallest to largest. In this paper we consider the problem of Finding the weighted kth smallest element of the multiset X + X= {X(i) + X(j):1≦ i≦ j ≦n}, in which X(i) + X(j)has weight w(i, j) = a(j-i+1) — a(j-i), where 0 = a(0)≦a(l)≦ ⃛ ≦a(n)≠0 are a set of integers called scores. We derive relations involving the weights w(i,j) which can in principle be used to eliminate a number of elements of X+X which cannot possibly be the kth smallest, regardless of the distribution of X. These results are applied to Wilcoxon scores and to winsorized Wilcoxon scores. We describe a fast algorithm for finding the weighted kth smallest element in both cases.
Original language | English |
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Pages (from-to) | 19-35 |
Number of pages | 17 |
Journal | Journal of Statistical Computation and Simulation |
Volume | 31 |
Issue number | 1 |
DOIs | |
State | Published - Jan 1 1989 |
ASJC Scopus subject areas
- Statistics and Probability
- Modeling and Simulation
- Statistics, Probability and Uncertainty
- Applied Mathematics