Variable Bandwidth Kernel Density Estimation for Censored Data

Suaray, Kagba

doi:10.1080/15598608.2011.10412025

Cited by 3 publications

(1 citation statement)

References 25 publications

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“…With smoothing of the PDF in view, the literature documents a steady stream of continued efforts aimed at improving KM and the closely related Nelson–Aalen estimator. Kernel smoothing relies on careful selection of bandwidth (Ghorai & Susarla, ; Müller & Wang, ; Kulasekera et al, ; Kim et al, ; Suaray, ), and there are the usual associated studies on relevant asymptotic optimality and rates of convergence (Belitser & Levit, ; Lemdani & Ould‐Said, ). A related approach is Bezier curve smoothing, which depends on the choice of Bezier points (Kim et al, ).…”

Section: Introductionmentioning

confidence: 99%

An empirical saddlepoint approximation based method for smoothing survival functions under right censoring

et al. 2019

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The Kaplan–Meier (KM) estimator is ubiquitously used for estimating survival functions, but it provides only a discrete approximation at the observation times and does not deliver a proper distribution if the largest observation is censored. Using KM as a starting point, we devise an empirical saddlepoint approximation‐based method for producing a smooth survival function that is unencumbered by choice of tuning parameters. The procedure inverts the moment generating function (MGF) defined through a Riemann–Stieltjes integral with respect to an underlying mixed probability measure consisting of the discrete KM mass function weights and an absolutely continuous exponential right‐tail completion. Uniform consistency, and weak and strong convergence results are established for the resulting MGF and its derivatives, thus validating their usage as inputs into the saddlepoint routines. Relevant asymptotic results are also derived for the density and distribution function estimates. The performance of the resulting survival approximations is examined in simulation studies, which demonstrate a favourable comparison with the log spline method (Kooperberg & Stone, 1992) in small sample settings. For smoothing survival functions we argue that the methodology has no immediate competitors in its class, and we illustrate its application on several real data sets. The Canadian Journal of Statistics 47: 238–261; 2019 © 2019 Statistical Society of Canada

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Section: Introductionmentioning

confidence: 99%

An empirical saddlepoint approximation based method for smoothing survival functions under right censoring

et al. 2019

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On the variable bandwidth kernel estimation of conditionalU-statistics at optimal rates in sup-norm

Bouzebda

Taachouche

2023

Physica A: Statistical Mechanics and its Applications

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An Improved Variable Kernel Density Estimator Based on L2 Regularization

Jin

Huang

2021

Mathematics

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The nature of the kernel density estimator (KDE) is to find the underlying probability density function (p.d.f) for a given dataset. The key to training the KDE is to determine the optimal bandwidth or Parzen window. All the data points share a fixed bandwidth (scalar for univariate KDE and vector for multivariate KDE) in the fixed KDE (FKDE). In this paper, we propose an improved variable KDE (IVKDE) which determines the optimal bandwidth for each data point in the given dataset based on the integrated squared error (ISE) criterion with the L2 regularization term. An effective optimization algorithm is developed to solve the improved objective function. We compare the estimation performance of IVKDE with FKDE and VKDE based on ISE criterion without L2 regularization on four univariate and four multivariate probability distributions. The experimental results show that IVKDE obtains lower estimation errors and thus demonstrate the effectiveness of IVKDE.

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Variable Bandwidth Kernel Density Estimation for Censored Data

Cited by 3 publications

References 25 publications

An empirical saddlepoint approximation based method for smoothing survival functions under right censoring

An empirical saddlepoint approximation based method for smoothing survival functions under right censoring

On the variable bandwidth kernel estimation of conditionalU-statistics at optimal rates in sup-norm

An Improved Variable Kernel Density Estimator Based on L2 Regularization

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