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Contents of PMS, Vol. 10, Fasc. 2,
pages 191 - 200
 

ASYMPTOTIC MULTIVARIATE NORMALITY FOR THE SUBSERIES VALUES OF A GENERAL STATISTIC FROM A STATIONARY SEQUENCE WITH APPLICATIONS TO NONPARAMETRIC CONFIDENCE INTERVALS

E. Carlstein

Abstract: Let (Z :- oo < i < +o o ) i be a strictly stationary a -mixing sequence with unknown marginal distributions and unknown dependence structure. Suppose that, given data ---> Z im := (Zi+1,Zi+2,...,Zi+m), the statistic ---> sim := sm(Z im) is a point estimator of the unknown parameter h. If a sample series --->Z0n is available, then the subseries values sim(0 < i < i+ m < n) may be used to construct a nonparametric confidence interval on h via either Student’s distribution or via the Typical Value principle. The asymptotic justification for both methods rests upon a more general result which provides necessary and sufficient conditions for asymptotic multivariate normality of subseries values.

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

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