A Non-Clustering Property of Stationary Sequences,
Abstract
For a random sequence of events, with indicator variables Xi, the behavior of the expectation E((X sub k +...+ K sub k + m-1)/(X sub 1 +...+X sub n)) for 1 < or = k < or = k + m - 1 < or = n can be taken as a measure of clustering of the events. When the measure on the X's is i.i.d., or even exchangeable, a symmetry argument shows that the expectation can be no more than m/n. When the X's are constrained only to a stationary sequence, the bound deteriorates, and depends on k as well. When m/n is small, the bound is roughly 2m/n for k near n/2 and is like (m/n) log n for k near l or n. The proof given is partly constructive, so these bounds are nearly achieved, even though there is room for improvement for other values of k. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1983
- Accession Number
- ADA129628
Entities
People
- Arif Zaman
Organizations
- Florida State University