On-line selection of \(c\)-alternating subsequences from a random sample (Q1952478)

Summary: A sequence \(X_1, X_2, \dots, X_n\) is a \(c\)-alternating sequence if any odd term is less than or equal to the next even term \(-c\) and if 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.