Hazard rate estimation on random fields

Consider observations (representing lifelengths) taken on a random field indexed by lattice points. Our purpose is to estimate the hazard rate r ( x ) , which is the rate of failure at time x for the survivors up to time x . We estimate r ( x ) by the nonparametric estimator constructed in terms of a kernel-type estimator for f ( x ) and the natural estimator for F ¯ ( x ) . Under some general mixing assumptions, the limiting distribution of the estimator at multiple points is shown to be multivariate normal. The result is useful in establishing confidence bands for r ( x ) with x in an interval.