Kernel estimates under association: strong uniform consistency

George G. Roussas

Statistics & Probability Letters, 1991, vol. 12, issue 5, 393-403

Abstract: Let X1, X2,... be associated random variables forming a strictly stationary sequence, and let f be the probability density function of X1. For r [greater-or-equal, slanted] 0 integer, let f(r) be the rth order derivative of f. Under suitable regularity conditions on a kernel function K, a sequence of bandwidths {hn}, the derivatives f(s), s = 0, 1,..., r, and the covariances Cov(X1, Xi), i [greater-or-equal, slanted] 2, the usual kernel estimate of f(r)(x) is shown to be strongly consistent, uniformly in x. An application is also presented in the estimation of the hazard rate. Finally, certain covergence rates are also discussed.

Keywords: Associated; random; variables; kernel; estimates; hazard; rate; strong; uniform; consistency; convergence; rates (search for similar items in EconPapers)
Date: 1991
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Citations: View citations in EconPapers (12)

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