Bagai, Isha ; Prakasa Rao, B. L. S. (1995) Kernel-type density and failure rate estimation for associated sequences Annals of the Institute of Statistical Mathematics, 47 (2). pp. 253-266. ISSN 0020-3157
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Official URL: http://www.springerlink.com/content/g3m1747v147621...
Related URL: http://dx.doi.org/10.1007/BF00773461
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 function f(x) and failure rate function r(x) for X1. Let fn (x) be a kerneltype estimator of f(x) based on X1 ,...,Xn. Properties of fn(x) are studied. Point wise 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 F̅n(x), the empirical survival function, is proposed. The estimator rn(x) is shown to be point wise strongly consistent as well as uniformly strongly consistent over some sets.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Springer. |
| Keywords: | Density Estimator; Failure-rate Estimator; Kernel Estimators; Associated Sequences |
| ID Code: | 37243 |
| Deposited On: | 12 Apr 2011 11:35 |
| Last Modified: | 07 Dec 2011 05:34 |
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