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Abstract
We analyze the optimal policy for the sequential selection of an alternating subsequence from a sequence of n independent observations from a continuous distribution F, and we prove a central limit theorem for the number of selections made by that policy. The proof exploits the backward recursion of dynamic programming and assembles a detailed understanding of the associated value functions and selection rules.
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On-Line Selection of c-Alternating Subsequences from a Random Sample. JOURNAL OF PROBABILITY AND STATISTICS 2013. [DOI: 10.1155/2013/623183] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
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.
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