ASYMPTOTIC NORMALITY OF CERTAIN FUNCTIONS DEFINED ON A MARKOV PROCESS.
WISCONSIN UNIV MADISON DEPT OF STATISTICS
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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.
- Statistics and Probability