Document Type : Research Article
Authors
1 University of Payam Noor, Tehran, Iran
2 Department of Statistics, Faculty of Sciences, University of Zanjan, Zanjan, Iran
Abstract
In this article, according to the importance of the hazard rate function criterion in the
evaluation of statistical distributions, its estimation methods are presented. Here, we suggest
estimators for the hazard rate function. First, we use the standard deconvolution kernel
density estimator and suggest a plug-in estimator. In the following we investigate asymptotic
behavior of our estimator. For another estimator, we construct the new estimation the
hazard rate function according plug-in and CDF. Finally, we consider the performance of
the suggested estimators by simulation. Mean square error of estimators λˆ(t, p), λˆ(t) and λˆ
c(t) present in tables 1 till 6.
Keywords
Institute of Statistical Mathematics, 63 (2011), pp. 1019-1046.
[2] D. Bagkavos, P. N. Patil, Local polynomial fitting in failure rate estimation, IEEE Transactions on Reliability, 56 (2008), pp. 126-163.
[3] R. J. Carroll, P. Hall, Optimal rates of convergence for deconvolving a density, Journal
of American Statistics Association, 83 (1988), pp. 1184-1186.
[4] I. Dattner, A. Goldenshluger, A. Juditsky, On deconvolution of distribution functions,
The Annals of Statisitcs, 39 (2011), pp. 2477-2501.
[5] A. Delaigle, J. Fan, R. J. Carroll, A Design-Adaptive Local Polynomial Estimator for
the Errors-in-Variables Problem, Journal of the American Statistical Association, 104 (2009),
pp. 348-359.
[6] J. Fan, I. Gijbels, Local Polynomial Modeling and Its Applications, Chapman and Hall,
London, 1996.
[7] J. Fan, Y. K. Truong, Nonparametric regression with errors in variables, The Annals of
Statistics, 21 (1993), pp. 1900-1925.
[8] E. Mammen, J. P. Nielsen, A general approach to the predictability issue in survival analyses, Biometrika, 94 (1998), pp. 873-892.
[9] A. Meister, Deconvolution Problems in Nonparametric Statistics, Springer, Berlin, Germany, 2009.
[10] H. G. Muller, J. L. Wang, W. B. Capra ¨ , From lifetables to hazard rates: The transformation approach, Biometrika, 84 (1997), pp. 881-892.
[11] J. P. Nielsen, Marker dependent hazard estimation from local linear estimation, Scandinavian Actuarial Journal, 2 (1998), pp. 113-124.
[12] J. P. Nielsen, C. G. Tanggaard, Boundary and bias correction in kernel hazard estimation,
Scandinavian Journal of Statistics, 28 (2001), pp. 675-698.
[13] J. P. Nielsen, C. Tanggaard, C. Jones, Local linear density estimation for filtered survival
data, Statistics, 42 (2009), pp. 167-186.
[14] G. Pulcini, Modeling the failure data of a repairable equipment with bathtub type failure
intensity, Reliability Engineering and System Safety, 71 (2001), pp. 209-218.
[15] B, Rai, N. Singh, Customer-rush near warranty expiration limit and nonparametric hazard
rate estimation from known mileage accumulation rates, IEEE Transactions on Reliability,
55 (2006), pp. 480-489.
[16] L. A, Stefanski, R. J. Carroll, Deconvoluting Kernel Density Estimators, Statistics: A
Journal of Theoretical and Applied Statistics, 21 (1990), pp. 169-184.
[17] M. P. Wand, Data-based choice of histogram bin width, The American Statistician, 51 (1997),
pp. 59-64.
[18] J. L. Wang, H. G. Muller, W. B. Capra , Analysis of oldest-old mortality: Lifetables
revisited, Annals of Statitics, 28 (1998), pp. 126-163.