Nonparametric estimation of hazard functions and their derivatives under truncation model

Gürler, Ülkü; Wang, Jane-Ling

doi:10.1007/bf00775812

Cited by 6 publications

(2 citation statements)

References 21 publications

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“…Somewhat more recently, Gürler and Wang (1993) examine hazard functions and their derivatives for nonparametric kernel estimators. Similarly, they again assume continuity of G in proving asymptotic normality.…”

Section: Literature Reviewmentioning

confidence: 99%

Estimating a distribution function for discrete data subject to random truncation with an application to structured finance

Lautier

Pozdnyakov²,

Yan³

2021

Preprint

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The literature for estimating a distribution function from truncated data is extensive, but it has given little attention to the case of discrete data over a finite number of possible values. We examine the Woodroofe-type estimator in this case and prove that the resulting vector of hazard rate estimators is asymptotically normal with independent components. Asymptotic normality of the survival function estimator is then established. Sister results for the truncation random variable are also proved. Further, a hypothesis test for the shape of the distribution function based on our results is presented. Such a test is useful to formally test the stationarity assumption in length-biased sampling. The finite sample performance of the estimators are investigated in a simulation study. We close with an application to an automotive lease securitization.

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Section: Literature Reviewmentioning

confidence: 99%

Estimating a distribution function for discrete data subject to random truncation with an application to structured finance

Lautier

Pozdnyakov²,

Yan³

2021

Preprint

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“…(A4) The kernel function ( ) K x is a continuous function of bounded variation and with bounded support [ 1,1] − , say. Let…”

Section: Asymptotic Propertiesmentioning

confidence: 99%

On local polynomial estimation of hazard rates and their derivatives under left truncation and right censoring models

Yuan¹

2018

BBIJ

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Estimating hazard rate function is an important problem in survival analysis. There are some estimation approaches based on kernel smoothing. However, they suffer from the boundary effects or need high order kernels, which increases the mean squared error. We introduce local polynomial estimators of hazard rates and their derivatives for the left truncation and right censoring models. The estimators have favorable properties similar to those of local polynomial regression estimators. Asymptotic expressions for the mean squared errors (AMSE's) are obtained. Consistency and joint asymptotic normality of the local polynomial estimators are established. A data-based local bandwidth selection rule is proposed. X X On local polynomial estimation of hazard rates and their derivatives under left truncation and right censoring models 200 Copyright: ©2018 Jiang et al. Citation: Jiang J, Chen L, Yuan Y. On local polynomial estimation of hazard rates and their derivatives under left truncation and right censoring models.

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Hazard Rate Estimation

Veraverbeke¹

2005

Encyclopedia of Statistical Sciences

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Nonparametric estimation of hazard functions and their derivatives under truncation model

Cited by 6 publications

References 21 publications

Estimating a distribution function for discrete data subject to random truncation with an application to structured finance

Estimating a distribution function for discrete data subject to random truncation with an application to structured finance

On local polynomial estimation of hazard rates and their derivatives under left truncation and right censoring models

Hazard Rate Estimation

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