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:

1967-04-01

Pagination or Media Count:

21.0

Abstract:

In the present paper it is first proved that, under essentially the same conditions, the quotients summation from m1 to m-n of g sub msummation from m1 to mn of f sub m and summation from m1 to mn of f sub msummation from m1 to mn 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, j1,...,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