Let random points X1,..., Xn be sampled in strict sequence from a continuous product distribution on Euclidean d-space. At the time Xj 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 γn1/(d+1) and give the exact value of γ. This extends the √2n result by Samuels and Steele for d = 1.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty