### ISHA BAGAI1 AND B. L. S. PRAKASA RAO2

1 Indian Statistical Institute, 7, S. J. S. Sansanwal Marg, New Delhi-110016, India
2 Indian Statistical Institute, 203 Barrackpore Trunk Road, Calcutta 700 035, India

(Received August 22, 1991; revised August 25, 1994)

Abstract.    Let {Xn, n > 1} be a strictly stationary sequence of associated random variables defined on a probability space (Omega, \cal B, \cal P) with probability density function f(x) and failure rate function r(x) for X1. Let fn(x) be a kernel-type estimator of f(x) based on X1, ···, Xn. Properties of fn(x) are studied. Pointwise strong consistency and strong uniform consistency are established under a certain set of conditions. An estimator rn(x) of r(x) based on fn(x) and \bar Fn(x), the empirical survival function, is proposed. The estimator rn(x) is shown to be pointwise strongly consistent as well as uniformly strongly consistent over some sets.

Key words and phrases:    Density estimator, failure-rate estimator, kernel estimators, associated sequences.

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