Summary
From among the numerous choices of nonparametric estimate of failure rate, we restrict consideration to that based on kernel estimates of density and distribution function, which has the major advantage of being continuous. We propose a solution to the bandwidth selection problem for this form of hazard estimate and asymptotic properties of the selected bandwidth are given.
Similar content being viewed by others
References
Ahmad, I. A.. (1976). Uniform strong convergence of the generalized failure rate estimate.Bull. Math. Statist. 17, 77–84.
Gonzalez-Manteiga, W. and Cadarso-Suarez, C.. (1994). Asymptotic properties of a generalized Kaplan-Meier estimator with some applications.Nonparametric Statist. 4, 65–78.
Grégoire, G.. (1993). Least squares cross-validation for counting process intensities.Scandinavian J. Statist. 20, 343–360.
Györfi, L., Härdle, W., Sarda, P. and Vieu, P. (1989).Nonparametric Curve Estimation from Time Series. Lectures Notes in Statistics60. Berlin: Springer.
Härdle, W. and Marron, J. S., (1985). Optimal bandwidth selection in nonparametric regression estimation.Ann. Statist. 13, 1465–1481.
Hart, J. and Vieu, P.. (1990). Data-driven bandwidth choice for density estimation based on dependent data.Ann. Statist. 18, 873–890.
Hassani, S., Sarda, P. and Vieu, P. (1986). Approche non paramétrique en thÈorie de la fiabilité: revue bibliographique.Revue de Statistique Appliquée 35, 27–41.
Lejeune, M. and Sarda, P. (1992). Smooth estimation of distribution and density functions.Comp. Statist. and Data Analysis 14, 457–471.
Marron, J. S. and Härdle, W. (1986). Random approximations of some measure of accuracy in nonparametric curve estimation.J. Multivariate Analysis 19, 1–13.
Murthy, V. K. (1965). Estimation of jumps, reliability and hazard rate.Ann. Statist. 36, 1032–1040.
Patil, P. N. (1993a). Bandwidth choice for nonparametric hazard rate estimation.J. Statist. Planning and Inference 35, 15–30.
Patil, P. N. (1993b). On the least squares cross-validation bandwidth in hazard rate estimation.Ann. Statist. 21, 1792–1810.
Patil, P. N., Wells, M. T. and Marron, J. S. (1994). Some heuristic of kernel based estimators of ratio functions.Nonparametric Statist. 4, 203–209.
Sarda, P. (1991). Estimating smooth distribution function.Proc. NATO Advanced Study on Nonparametric Functional Estimation and Related Topics (G. G. Roussas, ed.) Dordrecht: Kluwer, 271–283.
Sarda, P. and Vieu, P. (1989). Estimation non paramétrique de la fonction de hasard.Cahiers du C.E.R.O. 31, 241–265.
Sarda, P. and Vieu, P. (1991). Smoothing parameter selection in hazard estimation.Statist. and Prob. Lett. 11, 429–434.
Shirahata, S. and Chu, I. S. (1992). Integrated square errors of kernel type estimators of disribution functions.Ann. Inst. Statist. Math. 44, 579–591.
Singpurwalla, N. D. and Wong, M. Y. (1983). Kernel estimators of the failure rate and density estimation: an analogy.J. Appl. Statist. 78, 478–481.
Vieu, P. (1991). Quadratics errors for nonparametric estimates under dependence.J. Multivariate Analysis 39, 324–347.
Watson, G. S. and Leadbetter, M. R. (1964a). Hazard analysis I.Biometrika 51, 175–184.
Watson, G. S. and Leadbetter, M. R. (1964b). Hazard analysis II.Sankhyā A 26, 110–116.
Winter, B. B. (1979). Convergence rate of perturbed empirical distribution function.J. Appl. Prob. 16, 163–173.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Youndjé, É., Sarda, P. & Vieu, P. Optimal smooth hazard estimates. Test 5, 379–394 (1996). https://doi.org/10.1007/BF02562624
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02562624