Asymptotic normality of a smooth estimate of a random field distribution function under association

George G. Roussas

Statistics & Probability Letters, 1995, vol. 24, issue 1, 77-90

Abstract: Let Zd be the lattice of points in d with integer coordinates, and let {Xn}, n [epsilon] Zd, be a random field of real-valued translation invariant random variables with unknown distribution function F. For u and v in Zd with u [infinity] as N --> [infinity], I = 1, ..., d. On the basis of the random variables Xn, n [epsilon] B0k(N), let be a smooth kernel-type estimate of F. Under suitable regularity conditions, including that of association, it is shown that , properly normalized and centered, is asymptotically normal with specified parameters.

Keywords: Random; field; Positive; or; negative; association; Positive; or; negative; quadrant; dependence; Stationarity; Empirical; distribution; function; Smooth; estimate; of; a; distribution; function; Asymptotic; normality (search for similar items in EconPapers)
Date: 1995
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Citations: View citations in EconPapers (8)

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