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February 2000 Sequential selection of an increasing sequence from a multidimensional random sample
Yuliy M. Baryshnikov, Alexander V. Gnedin
Ann. Appl. Probab. 10(1): 258-267 (February 2000). DOI: 10.1214/aoap/1019737672

Abstract

Let random points $X_1,\dots, X_n$ be sampled in strict sequence from a continuous product distribution on Euclidean $d$-space. At the time $X_j$ is observed it must be accepted or rejected. The subsequence of accepted points must increase in each coordinate. We show that the maximum expected length of a subsequence selected is asymptotic to $\gamma n^{1/(d+1)}$ and give the exact value of $\gamma$. This extends the $\sqrt{2n}$ result by Samuels and Steele for $d = 1$.

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Yuliy M. Baryshnikov. Alexander V. Gnedin. "Sequential selection of an increasing sequence from a multidimensional random sample." Ann. Appl. Probab. 10 (1) 258 - 267, February 2000. https://doi.org/10.1214/aoap/1019737672

Information

Published: February 2000
First available in Project Euclid: 25 April 2002

zbMATH: 1163.60310
MathSciNet: MR1765211
Digital Object Identifier: 10.1214/aoap/1019737672

Subjects:
Primary: 06A10, 60G40, 62L15

Rights: Copyright © 2000 Institute of Mathematical Statistics

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Vol.10 • No. 1 • February 2000
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