A local linear estimation of conditional hazard function in censored data

Kim, Choongrak; Oh, Minkyung; Yang, Seong J.; Choi, Hyemi

doi:10.1016/j.jkss.2010.03.002

Cited by 11 publications

(13 citation statements)

References 24 publications

(35 reference statements)

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“…Both of these two new feasible methods were shown to work well in finite sample studies with continuous data, but indirect cross-validation was shown to be superior in the practical study of old-age mortality. The difference between the local linear estimator by Nielsen (1998) and the LLLC estimator (which generalises the estimators of Spierdijk (2008) and Kim et al (2010)) is that the latter is local constant in the time direction. This simplification can have dramatic effects around the boundary regions, where the fully local linear estimator is shown to work much better than the LLLC estimator.…”

Section: Resultsmentioning

confidence: 99%

“…Simply splitting the hazard estimator into occurrences and exposures as we do above makes it possible to analyse them separately and restrict the visual representation of the hazard to the area of interest. A generalisation of the recent estimators of Spierdijk (2008) and Kim et al (2010) to our counting process framework are obtained by the above minimisation principle when it is adjusted to be local linear in the covariates only and local constant in the time direction. We call this estimator the local linear local constant estimator, or the LLLC estimator.…”

Section: The Local Linear Principle For Multivariate Kernel Hazard Esmentioning

confidence: 99%

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Bandwidth selection in marker dependent kernel hazard estimation

Pérez

Janys

Miranda

et al. 2013

Computational Statistics & Data Analysis

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This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent repository link AbstractPractical estimation procedures for local linear estimation of an unrestricted failure rate when more information is available than just time are developed. This extra information could be a covariate and this covariate could be a time series. Time dependent covariates are sometimes called markers, and failure rates are sometimes called hazards, intensities or mortalities. It is shown through simulations and a practical example that the fully local linear estimation procedure exhibits an excellent practical performance. Two different bandwidth selection procedures are developed. One is an adaptation of classical cross-validation, and the other one is indirect cross-validation. The simulation study concludes that classical cross-validation works well on continuous data while indirect cross-validation performs only marginally better. However, cross-validation breaks down in the practical data application to old-age mortality. Indirect cross-validation is thus shown to be superior when selecting a fully feasible estimation method for marker dependent hazard estimation.

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Section: Resultsmentioning

confidence: 99%

Section: The Local Linear Principle For Multivariate Kernel Hazard Esmentioning

confidence: 99%

Bandwidth selection in marker dependent kernel hazard estimation

Pérez

Janys

Miranda

et al. 2013

Computational Statistics & Data Analysis

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“…However, in these papers, it is assumed that the observations are complete. the local linear estimator, which extends the asymptotic distribution of the local linear estimator of the conditional density function in Kim et al(2010) from the i.i.d. assumption to the α-mixing setting.…”

Section: Introductionmentioning

confidence: 95%

Non parametric estimation of the conditional density function with right-censored and dependent data

Xiong

2019

Communications in Statistics - Theory and Methods

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In this paper, we study the local constant and the local linear estimators of the conditional density function with right-censored data which exhibit some type of dependence. It is assumed that the observations form a stationary α−mixing sequence. The asymptotic normality of the two estimators is established, which combined with the condition that lim n→∞ nh n b n = ∞ implies the consistency of the two estimators and can be employed to construct confidence intervals for the conditional density function. The result on the local linear estimator of the conditional density function in Kim et al. (2010) is relaxed from the i.i.d. assumption to the α−mixing setting, and the result on the local linear estimator of the conditional density function in Spierdijk (2008) is relaxed from the ρ-mixing assumption to the α−mixing setting. Finite sample behavior of the estimators is investigated by simulations.In Survival Analysis or Reliability, right-censored data are often encountered. There is substantial literature on nonparametric modelling of right-censored data. For example, Guessoum and Ould Saïd (2008, 2012 and Liang and Iglesias-Pérez (2018) considered the estimation of the conditional mean function. This paper focuses on the estimation of the conditional density function, and there are some papers on this topic such as Spierdijk (2008), Kim et al. (2010), Liang and Peng (2010) and Khardani and Semmar (2014). Spierdijk (2008) studied one version of local linear estimators of the conditional density function with stationary ρ−mixing observations, while Kim et al. (2010) proposed another version of local linear estimators with different weights in the independent and identical distributed (i.i.d.) case. The weights are random quantities determined by the Kaplan-Meier estimation of the survival function of the censoring times, and they indeed include the equal weights used by Spierdijk (2008). Those weights have been also adopted by many papers including Guessoum and Ould Saïd (2008, 2012, Liang and Peng (2010) andLiang and de Uña-Álvarez (2011). Especially, Liang and Peng (2010) derived the asymptotic normality and the Berry-Esseen type bound for the kernel estimator of the conditional density function with stationary α-mixing observations. It should be noted that the kernel estimator proposed by Liang and Peng (2010) is a single-smoothing estimator (smoothing the covariates only) of the conditional density function, while the local linear estimator proposed by Kim et al. (2010) is a double-smoothing estimator (smoothing both the response variable and the covariates). In fact, compared with the single-smoothing estimator, the double-smoothing estimator not only appears closer to a conditional density function, but also has more flexibility to reduce the meansquared error when the optimal bandwidths are selected. However, the asymptotic distribution of the local linear estimator of the conditional density function in Kim et al. (2010) was investigated in the i.i.d. setting (although Kim et al. (2010) established the asym...

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“…Nielsen and Linton [12] proposed the external estimator for the conditional hazard function using a counting process. Spierdijk [13] and Kim et al [14] studied the local linear estimator for a conditional case.…”

Section: Introductionmentioning

confidence: 99%

Comparison of parametric and semiparametric survival regression models with kernel estimation

Selingerová

Katina

Horová

2021

Journal of Statistical Computation and Simulation

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The modelling of censored survival data is based on different estimations of the conditional hazard function. When survival time follows a known distribution, parametric models are useful. This strong assumption is replaced by a weaker in the case of semiparametric models. For instance, the frequently used model suggested by Cox is based on the proportionality of hazards. These models use non-parametric methods to estimate some baseline hazard and parametric methods to estimate the influence of a covariate. An alternative approach is to use smoothing that is more flexible. In this paper, two types of kernel smoothing and some bandwidth selection techniques are introduced. Application to real data shows different interpretations for each approach. The extensive simulation study is aimed at comparing different approaches and assessing their benefits. Kernel estimation is demonstrated to be very helpful for verifying assumptions of parametric or semiparametric models and is able to capture changes in the hazard function in both time and covariate directions.

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A local linear estimation of conditional hazard function in censored data

Cited by 11 publications

References 24 publications

Bandwidth selection in marker dependent kernel hazard estimation

Bandwidth selection in marker dependent kernel hazard estimation

Non parametric estimation of the conditional density function with right-censored and dependent data

Comparison of parametric and semiparametric survival regression models with kernel estimation

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