A Weak Convergence Theorem for Order Statistics from Strong-Mixing Processes.
Abstract
The paper provides sufficient conditions for the weak convergence in the Skorohod space D sup d (a,b) of the processes ((Y sub (1,(nt)) - b sub n)/a sub n, (y sub (2,(nt)) - b sub n)/a sub n,..., (Y sub (d,(nt)) - b sub n)/a sub n), 0 < a = or < t = or < b where Y sub (i,n) is the ith largest among (X sub 1, X sub 2,..., X sub n), (a sub n) and (b sub n) are normalizing constants, and < (X sub n) : n = or > 1 > is a stationary strong-mixing sequence of random variables. Under the conditions given, the weak limits of these processes coincide with those obtained when < (X sub n) : n = or > 1 > is a sequence of independent identically distributed random variables. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1970
- Accession Number
- AD0722833
Entities
People
- Roy E. Welsch
Organizations
- Massachusetts Institute of Technology