Optimal online selection of a monotone subsequence: A central limit theorem
Consider a sequence of n independent random variables with a common continuous distribution F, and consider the task of choosing an increasing subsequence where the observations are revealed sequentially and where an observation must be accepted or rejected when it is first revealed. There is a unique selection policy πn∗ that is optimal in the sense that it maximizes the expected value of Ln(πn∗), the number of selected observations. We investigate the distribution of Ln(πn∗); in particular, we obtain a central limit theorem for Ln(πn∗) and a detailed understanding of its mean and variance for large n. Our results and methods are complementary to the work of Bruss and Delbaen (2004) where an analogous central limit theorem is found for monotone increasing selections from a finite sequence with cardinality N where N is a Poisson random variable that is independent of the sequence.
Duke Scholars
Altmetric Attention Stats
Dimensions Citation Stats
Published In
DOI
ISSN
Publication Date
Volume
Issue
Start / End Page
Related Subject Headings
- Statistics & Probability
- 4905 Statistics
- 4901 Applied mathematics
- 1502 Banking, Finance and Investment
- 0104 Statistics
- 0102 Applied Mathematics
Citation
Published In
DOI
ISSN
Publication Date
Volume
Issue
Start / End Page
Related Subject Headings
- Statistics & Probability
- 4905 Statistics
- 4901 Applied mathematics
- 1502 Banking, Finance and Investment
- 0104 Statistics
- 0102 Applied Mathematics