Kernel-type density and failure rate estimation for associated sequences

Let {X _n ,n1} be a strictly stationary sequence of associated random variables defined on a probability space (,B, P) with probability density functionf(x) and failure rate functionr(x) forX ₁. Letf _n (x) be a kerneltype estimator off(x) based onX ₁,...,X _n . Properties off _n (x) are studied. Pointwise strong consistency and strong uniform consistency are established under a certain set of conditions. An estimatorr _n (x) ofr(x) based onf _n (x) andF _n (x), the empirical survival function, is proposed. The estimatorr _n (x) is shown to be pointwise strongly consistent as well as uniformly strongly consistent over some sets.