scholarly journals Bootstrap Selection of the Smoothing Parameter in Nonparametric Hazard Rate Estimation

1996 ◽  
Vol 91 (435) ◽  
pp. 1130 ◽  
Author(s):  
W. Gonzalez-Manteiga ◽  
R. Cao ◽  
J. S. Marron
Keyword(s):  
Hazard Rate ◽  
Smoothing Parameter ◽  
Rate Estimation ◽  
Selection Of

Double-smoothing in Kernel Hazard Rate Estimation

2008 ◽  
Vol 47 (02) ◽  
pp. 167-173 ◽  
Author(s):  
A. Pfahlberg ◽  
O. Gefeller ◽  
R. Weißbach
Keyword(s):  
Hazard Rate ◽  
Nearest Neighbor ◽  
Bandwidth Selection ◽  
Study Data ◽  
Computational Effort ◽  
Finite Sample ◽  
Adaptive Smoothing ◽  
Rate Estimation ◽  
Data Adaptive ◽  
Double Smoothing

Summary Objectives: In oncological studies, the hazard rate can be used to differentiate subgroups of the study population according to their patterns of survival risk over time. Nonparametric curve estimation has been suggested as an exploratory means of revealing such patterns. The decision about the type of smoothing parameter is critical for performance in practice. In this paper, we study data-adaptive smoothing. Methods: A decade ago, the nearest-neighbor bandwidth was introduced for censored data in survival analysis. It is specified by one parameter, namely the number of nearest neighbors. Bandwidth selection in this setting has rarely been investigated, although the heuristical advantages over the frequently-studied fixed bandwidth are quite obvious. The asymptotical relationship between the fixed and the nearest-neighbor bandwidth can be used to generate novel approaches. Results: We develop a new selection algorithm termed double-smoothing for the nearest-neighbor bandwidth in hazard rate estimation. Our approach uses a finite sample approximation of the asymptotical relationship between the fixed and nearest-neighbor bandwidth. By so doing, we identify the nearest-neighbor bandwidth as an additional smoothing step and achieve further data-adaption after fixed bandwidth smoothing. We illustrate the application of the new algorithm in a clinical study and compare the outcome to the traditional fixed bandwidth result, thus demonstrating the practical performance of the technique. Conclusion: The double-smoothing approach enlarges the methodological repertoire for selecting smoothing parameters in nonparametric hazard rate estimation. The slight increase in computational effort is rewarded with a substantial amount of estimation stability, thus demonstrating the benefit of the technique for biostatistical applications.

Hazard rate estimation for call center customer patience time

2020 ◽  
Vol 52 (8) ◽  
pp. 890-903
Author(s):  
Han Ye ◽  
Lawrence D. Brown ◽  
Haipeng Shen
Keyword(s):  
Call Center ◽  
Hazard Rate ◽  
Rate Estimation

Smoothing Noisy Data Using Dynamic Programming and Generalized Cross-Validation

1988 ◽  
Vol 110 (1) ◽  
pp. 37-41 ◽  
Author(s):  
C. R. Dohrmann ◽  
H. R. Busby ◽  
D. M. Trujillo
Keyword(s):  
Dynamic Programming ◽  
Cross Validation ◽  
Present Model ◽  
Noisy Data ◽  
Smoothing Parameter ◽  
Spline Functions ◽  
General Context ◽  
Simple Extension ◽  
Generalized Cross Validation ◽  
Selection Of

Smoothing and differentiation of noisy data using spline functions requires the selection of an unknown smoothing parameter. The method of generalized cross-validation provides an excellent estimate of the smoothing parameter from the data itself even when the amount of noise associated with the data is unknown. In the present model only a single smoothing parameter must be obtained, but in a more general context the number may be larger. In an earlier work, smoothing of the data was accomplished by solving a minimization problem using the technique of dynamic programming. This paper shows how the computations required by generalized cross-validation can be performed as a simple extension of the dynamic programming formulas. The results of numerical experiments are also included.

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