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

A sequence is a -alternating sequence if any odd term is less than or equal to the next even term and the any even term is greater than or equal to the next odd term , where is a nonnegative constant. In this paper, we present an optimal on-line procedure to select a -alternating subsequence from a symmetric distributed random sample. We also give the optimal selection rate when the sample size goes to infinity.