A Review on Smoothing Methods for the Estimation of the Hazard Rate Based on Kernel Functions

Gefeller, Olaf; Michels, Paul

doi:10.1007/978-3-662-26811-7_63

Cited by 15 publications

(9 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For a survey, see Singpurwalla and Wong (1983), Hassani, Sarda, and Vieu (1986), Gefeller and Michels (1992), and Padgett (1988). Roughly speaking, two different methods have been proposed to estimate the hazard rate in a nonparametric way.…”

Section: Literature Reviewmentioning

confidence: 99%

Nonparametric conditional hazard rate estimation: A local linear approach

Spierdijk

2008

Computational Statistics & Data Analysis

View full text Add to dashboard Cite

Parametric and semiparametric methods often fail to capture the right shape of the conditional hazard rate in survival analysis. In this paper we propose a new and intuitive nonparametric estimator for the conditional hazard rate, based on local linear estimation techniques. This estimator can deal with both censored and uncensored data. We show that the local linear hazard rate estimator is consistent and asymptotically normal distributed. Moreover, we derive plug-in bandwidths based on normal and uniform reference distributions. We show that these bandwidths perform reasonably well, even when the underlying distributional assumptions are violated. We illustrate the use of the nonparametric local linear hazard rate estimator and the bandwidth selection method in several simulation experiments and in two applications to real-life data.

show abstract

Section: Literature Reviewmentioning

confidence: 99%

Nonparametric conditional hazard rate estimation: A local linear approach

Spierdijk

2008

Computational Statistics & Data Analysis

View full text Add to dashboard Cite

show abstract

“…For the cubics, we set h (t)"at#bt#ct#d, and we speci"ed h (0), the locations of the extrema, and the magnitude of the "rst extremum. We generated uniform numbers u G over [0,1] and used the inverse function t G "S\(u G ) to generate random times for the given distribution. To implement random censorship, we independently generated uniform censoring times on the interval [0, ;], where ; was selected to achieve a given proportion of censoring (on average).…”

Section: Simulation Experimentsmentioning

confidence: 99%

Hazard function estimators: a simulation study

1999

View full text Add to dashboard Cite

Kernel‐based methods for the smooth, non‐parametric estimation of the hazard function have received considerable attention in the statistical literature. Although the mathematical properties of the kernel‐based hazard estimators have been carefully studied, their statistical properties have not. We reviewed various kernel‐based methods for hazard function estimation from right‐censored data and compared the statistical properties of these estimators through computer simulations. Our simulations covered seven distributions, three levels of random censoring, four types of bandwidth functions, two sample sizes and three types of boundary correction. We conducted a total of 504 simulation experiments with 500 independent samples each. Our results confirmed the advantages of two recent innovations in kernel estimation – boundary correction and locally optimal bandwidths. The median relative improvement (decrease) in mean square error over fixed‐bandwidth estimators without boundary correction was 3 per cent for fixed‐bandwidth estimators with left boundary correction, 52 per cent locally optimal bandwidths without boundary correction, and 66 per cent for locally optimal bandwidths with left boundary correction. The locally optimal bandwidth estimators with left boundary correction also outperformed three previously published and publicly available algorithms, with median relative improvements in mean square error of 31 per cent, 77 per cent and 80 per cent. Copyright © 1999 John Wiley & Sons, Ltd.

show abstract

“…The hazard function λ(•) has been extensively studied in the literature. The estimation by means of kernel methods has been investigated by Gefeller and Dette (1992), Gefeller and Michels (1992), Patil (1993), Müller and Wang (1994) and González-Manteiga et al (1996), among others. The PGK estimator for the hazard function λ(•) that we proposed in the previous section is…”

Section: Guided Kernel Hazard Estimator With An Estimated Guidementioning

confidence: 99%

Parametrically guided nonparametric density and hazard estimation with censored data

Talamakrouni

Keilegom

Ghouch

2016

Computational Statistics & Data Analysis

View full text Add to dashboard Cite

The parametrically guided kernel smoother is a promising nonparametric estimation approach that aims to reduce the bias of the classical kernel density estimator without increasing its variance. Theoretically, the estimator is unbiased if a correct parametric guide is used, which can never be achieved by the classical kernel estimator even with an optimal bandwidth. The estimator is generalized to the censored data case and used for density and hazard function estimation. The asymptotic properties of the proposed estimators are established and their performance is evaluated via finite sample simulations. The method is also applied to data coming from a study where the interest is in the time to return to drug use.

show abstract

A Review on Smoothing Methods for the Estimation of the Hazard Rate Based on Kernel Functions

Cited by 15 publications

References 20 publications

Nonparametric conditional hazard rate estimation: A local linear approach

Nonparametric conditional hazard rate estimation: A local linear approach

Hazard function estimators: a simulation study

Parametrically guided nonparametric density and hazard estimation with censored data

Contact Info

Product

Resources

About