Smoothed bootstrap bandwidth selection for nonparametric hazard rate estimation

Barbeito, Inés; Cao, Ricardo

doi:10.1080/00949655.2018.1532512

Cited by 6 publications

(8 citation statements)

References 26 publications

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“…In the study by Barbeito and Cao () and Barbeito and Cao (), among others, the performance of several bandwidth selectors is illustrated with an application to some real data sets in the context of density and hazard rate estimation, respectively.…”

Section: Bootstrap Bandwidth Selection In Nonparametric Curve Estimationmentioning

confidence: 99%

“…In the context of hazard rate estimation in a classical independent setup, just one approach has dealt with the use of bootstrap techniques to select the bandwidth parameter. In particular, so as to get rid of the randomness of the denominator of the classical hazard rate estimator, (Barbeito & Cao, ) proposed two proxy estimators of the hazard rate function. They are not real estimators, but theoretical approximations.…”

Section: Data Generating Processesmentioning

confidence: 99%

“…However, in some cases such as the classical hazard rate estimator, this does not happen and getting rid of the randomness of the denominator leads to obtaining a simpler stochastic expression. In this sense, Barbeito and Cao () and Barbeito et al () came up with the idea of considering a proxy estimator. It is not a real estimation, but some theoretical approximation.…”

Section: Computing/approximating the Bootstrap Criterion Functionmentioning

confidence: 99%

“…Moreover, this proxy estimator is similar to the real one in the bandwidth region in which both of them attain their minimum. For the sake of brevity, we focus on the proposal by Barbeito and Cao () for hazard rate estimation. In order to get rid of the randomness of the denominator of the classical hazard rate estimator, since it complicates the computation of a closed expression for the bootstrap MISE, these authors consider the following proxy estimator.

{\overset{false˜}{r}}_{h, 1} ((), x) = \frac{{\overset{false^}{f}}_{h} ((), x)}{1 - F ((), x)},

where

{\overset{false^}{f}}_{h} ((), x)

stands for the classical nonparametric KDE (see Parzen, ; Rosenblatt, ).…”

Section: Computing/approximating the Bootstrap Criterion Functionmentioning

confidence: 99%

“…As it can be seen in Equation , the denominator depends on the underlying theoretical distribution function F . Considering now the proxy estimator defined in Equation , the computation of a closed expression for the bootstrap MISE turns out to be feasible, as it can be seen in Barbeito and Cao (). A more accurate proxy estimator given by:

{\overset{false˜}{r}}_{h, 2} ((), x) = ((), {\overset{false^}{r}}_{h} ((), x) - r ((), x)) \frac{1 - {\overset{false^}{F}}_{h} ((), x)}{1 - F ((), x)} + r ((), x),

was also studied by Barbeito and Cao ().…”

Section: Computing/approximating the Bootstrap Criterion Functionmentioning

confidence: 99%

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Nonparametric curve estimation and bootstrap bandwidth selection

Barbeito

Cao

2019

WIREs Computational Stats

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Over the last four decades, the bootstrap method has been considered so as to define data-driven bandwidth selectors for nonparametric curve estimation. An extensive and updated review of bootstrap methods used to select the smoothing parameter for the nonparametric estimation of several curves has been carried out. Different data generating processes have been profoundly reviewed, such as the classical independent and identically distributed setup as well as dependent, censored, length-biased, grouped, missing or directional data, among others. Several curves have also been considered, such as the density, regression, hazard rate, intensity, latency, incidence, or distribution functions, among many others. It is worth mentioning that there exist situations where Monte Carlo methods are not needed when using the bootstrap for bandwidth selections. This idea has also been exploited to find closed expressions for the bootstrap version of criterion functions for some proxy of the real curve estimator. This article is categorized under:Statistical and Graphical Methods of Data Analysis > Bootstrap and Resampling

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Section: Bootstrap Bandwidth Selection In Nonparametric Curve Estimationmentioning

confidence: 99%

Section: Data Generating Processesmentioning

confidence: 99%

Section: Computing/approximating the Bootstrap Criterion Functionmentioning

confidence: 99%

{\overset{false˜}{r}}_{h, 1} ((), x) = \frac{{\overset{false^}{f}}_{h} ((), x)}{1 - F ((), x)},

where

{\overset{false^}{f}}_{h} ((), x)

stands for the classical nonparametric KDE (see Parzen, ; Rosenblatt, ).…”

Section: Computing/approximating the Bootstrap Criterion Functionmentioning

confidence: 99%

{\overset{false˜}{r}}_{h, 2} ((), x) = ((), {\overset{false^}{r}}_{h} ((), x) - r ((), x)) \frac{1 - {\overset{false^}{F}}_{h} ((), x)}{1 - F ((), x)} + r ((), x),

was also studied by Barbeito and Cao ().…”

Section: Computing/approximating the Bootstrap Criterion Functionmentioning

confidence: 99%

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Nonparametric curve estimation and bootstrap bandwidth selection

Barbeito

Cao

2019

WIREs Computational Stats

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Hazard regression with noncompactly supported bases

Brunel

Comte

2021

Can J Statistics

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In this article, we consider the problem of nonparametric hazard rate estimation in the presence of right‐censored observations. We provide a generalized risk bound for a regression‐type nonparametric estimator of the hazard function of interest. Under adequate integrability conditions, our bound is a generalization of estimation strategies specific to compactly supported bases to bases that are not necessarily compactly supported. We show that it encompasses previous compact‐support results and interestingly represents hazard rates as combinations of gamma functions. We discuss the model selection method, which comes out from the new terms of the risk bounds, and compare the performance of the new estimator to that of previous ones, when using a noncompact Laguerre basis. A real data example is also presented.

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Comments on: Data science, big data and statistics

Cao

2019

TEST

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The invited paper by Peña and Galeano is a very inspiring one. The authors analyze how Big Data is changing statisticians' minds by describing new statistical methods in seven areas: the emergence of new sources of information; visualization in high dimensions; multiple testing problems; analysis of heterogeneity; automatic model selection; estimation methods for sparse models; and merging network information with statistical models. They also compare the statistical view with the ones of Computer Science and Machine Learning and put a lot of emphasis in the emergence of the new field of Data Science. Two nice examples of Big Data statistical analysis are also included.When the reader goes through the paper, plenty of interesting ideas appear. The problems dealt with are also very inspiring, suggesting interesting aspects that surely will need deep insights in the future. Five of them are mentioned in the following subsections.

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Smoothed bootstrap bandwidth selection for nonparametric hazard rate estimation

Cited by 6 publications

References 26 publications

Nonparametric curve estimation and bootstrap bandwidth selection

Nonparametric curve estimation and bootstrap bandwidth selection

Hazard regression with noncompactly supported bases

Comments on: Data science, big data and statistics

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