On-Line Selection of c-Alternating Subsequences from a Random Sample

Abstract EN

A sequence X1,X2,…,Xn is a c-alternating sequence if any odd term is less than or equal to the next even term -c and the any even term is greater than or equal to the next odd term +c, where c is a nonnegative constant.

In this paper, we present an optimal on-line procedure to select a c-alternating subsequence from a symmetric distributed random sample.

We also give the optimal selection rate when the sample size goes to infinity.