Accession Number : AD0653271

Title :   ASYMPTOTIC NORMALITY OF CERTAIN FUNCTIONS DEFINED ON A MARKOV PROCESS.

Descriptive Note : Technical rept.,

Corporate Author : WISCONSIN UNIV MADISON DEPT OF STATISTICS

Personal Author(s) : Roussas,George G.

Report Date : APR 1967

Pagination or Media Count : 21

Abstract : In the present paper it is first proved that, under essentially the same conditions, the quotients (summation from m=1 to m-n of g sub m/summation from m=1 to m=n of f sub m) and (summation from m=1 to m=n of f sub m/summation from m=1 to m=n of g sub m) properly normalized, are also asymptotically normal. Next, the functions f and g are also considered to be dependent on n--the number of the random variables X sub j, j=1,...,n--and asymptotic normalities similar to the ones mentioned above are established under a number of conditions. The results obtained here are useful in statistical applications and are applied in the problem of non-parametric estimation in Markov processes.

Descriptors :   (*STATISTICAL PROCESSES, THEOREMS), FUNCTIONS(MATHEMATICS), PROBABILITY, INEQUALITIES, MATHEMATICS, THEORY

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE