A Weak Convergence Theorem for Order Statistics from Strong-Mixing Processes.
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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 na sub n, y sub 2,nt - b sub na sub n,..., Y sub d,nt - b sub na 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
- Statistics and Probability