Abstract
Let {X n ,n≥1} be a strictly stationary sequence of associated random variables defined on a probability space (Ω,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.
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Bagai, I., Prakasa Rao, B.L.S. Kernel-type density and failure rate estimation for associated sequences. Ann Inst Stat Math 47, 253–266 (1995). https://doi.org/10.1007/BF00773461
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DOI: https://doi.org/10.1007/BF00773461