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Full-Text Articles in Physical Sciences and Mathematics
Prophet Inequalities For Parallel Processes, Theodore P. Hill, D. P. Kennedy
Prophet Inequalities For Parallel Processes, Theodore P. Hill, D. P. Kennedy
Research Scholars in Residence
Generalizations of prophet inequalities for single sequences are obtained for optimal stopping of several parallel sequences of independent random variables. For example, if {Xi, j, 1 ≤ i ≤ n, 1 ≤ j < ∞} are independent non-negative random variables, then E(sup Xi,j) ≤ (n + 1) max sup {E(Xi,t): t is a stop rule for Xi,1, Xi,2, ...} and this bound is best possible. Applications are made to comparisons of the optimal expected returns of various alternative methods of stopping of parallel processes.
Optimal-Partitioning Inequalities In Classification And Multi-Hypotheses Testing, Theodore P. Hill, Y. L. Tong
Optimal-Partitioning Inequalities In Classification And Multi-Hypotheses Testing, Theodore P. Hill, Y. L. Tong
Research Scholars in Residence
Optimal-partitioning and minimax risk inequalities are obtained for the classification and multi-hypotheses testing problems. Best possible bounds are derived for the minimax risk for location parameter families, based on the tail concentrations and Levy concentrations of the distributions. Special attention is given to continuous distributions with the maximum likelihood ratio property and to symmetric unimodal continuous distributions. Bounds for general (including discontinuous) distributions are also obtained.