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. 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.