Optimal Sequential Selection of a Monotone Sequence From a Random Sample
نویسندگان
چکیده
منابع مشابه
Sequential Selection of a Monotone Subsequence from a Random Permutation
We find a two term asymptotic expansion for the optimal expected value of a sequentially selected monotone subsequence from a random permutation of length n. A striking feature of this expansion is that it tells us that the expected value of optimal selection from a random permutation is quantifiably larger than optimal sequential selection from an independent sequence of uniformly distributed ...
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Given a sequence of n independent random variables with common continuous distribution, we propose a simple adaptive online policy that selects a monotone increasing subsequence. We show that the expected number of monotone increasing selections made by such policy is within O(logn) of optimal. Our construction provides a direct and natural way for proving the O(logn)-optimality gap. An earlier...
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Given a sequence of n independent random variables with common continuous distribution, we propose a simple adaptive online policy that selects a monotone increasing subsequence. We show that the expected number of monotone increasing selections made by such a policy is within O(logn) of optimal. Our construction provides a direct and natural way for proving the O(logn)-optimality gap. An earli...
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We consider the problem of selecting sequentially a unimodal subsequence from a sequence of independent identically distributed random variables, and we find that a person doing optimal sequential selection does so within a factor of the square root of two as well as a prophet who knows all of the random observations in advance of any selections. Our analysis applies in fact to selections of su...
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A brief proof is given for an upper bound on expected length of the optimal on-line selection of a monotone subsequence from a finite random sequence. The bound is valid for all sample sizes and it is sharp for large samples. We also provide a bound on the variance of the length of the optimal subsequence. Mathematics Subject Classification (2000): Primary 60C05, Secondary 60G42
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 1981
ISSN: 0091-1798
DOI: 10.1214/aop/1176994265