Journal of Probability and Statistics
Volume 2013 (2013), Article ID 623183, 5 pages
http://dx.doi.org/10.1155/2013/623183
Research Article

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

Robert W. Chen,1 Larry A. Shepp,2 and Justín Ju-Chen Yang3

1Department of Mathematics, University of Miami, Coral Gables, FL 33124, USA
2Department of Statistics, Wharton School, University of Pennsylvania, Philadelphia, PA 19104, USA
3Department of Statistics, Harvard University, 1 Oxford Street, Cambridge, MA 02138-2901, USA

Received 24 August 2012; Accepted 4 January 2013

Academic Editor: Shein-chung Chow

Copyright © 2013 Robert W. Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.