Accession Number : AD0722833

Title :   A Weak Convergence Theorem for Order Statistics from Strong-Mixing Processes.

Descriptive Note : Technical rept.,

Corporate Author : MASSACHUSETTS INST OF TECH CAMBRIDGE OPERATIONS RESEARCH CENTER

Personal Author(s) : Welsch,Roy E.

Report Date : DEC 1970

Pagination or Media Count : 31

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)

Descriptors :   (*STATISTICAL ANALYSIS, THEOREMS), DISTRIBUTION FUNCTIONS, RANDOM VARIABLES, PROBABILITY, CONVERGENCE, THEOREMS, THESES

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE