Smoothing survival densities in practice

Pérez, M. Luz Gámiz; Miranda, María Dolores Martínez; Nielsen, Jens Perch

doi:10.1016/j.csda.2012.09.011

Cited by 10 publications

(3 citation statements)

References 24 publications

(18 reference statements)

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“…In particular when the results are as crystal clear as the finite sample results we are getting in this paper. The bandwidth selectors of this paper could potentially also carry over to other smoothing problems, see Soni, Dewan and Jain (2012) and Oliveira, Crujeiras and Rodríguez-Casal (2012) and Gámiz-Pérez, Martínez-Miranda and Nielsen (2012). The latter paper actually supports the use of Do-validation in survival smoothing and show its superiority to classical crossvalidation also in this case.…”

Section: Introductionsupporting

confidence: 62%

A comparative study of new cross-validated bandwidth selectors for kernel density estimation

Mammen,

Miranda,

Nielsen

et al. 2012

Preprint

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Recent contributions to kernel smoothing show that the performance of crossvalidated bandwidth selectors improve significantly from indirectness. Indirect crossvalidation first estimates the classical cross-validated bandwidth from a more rough and difficult smoothing problem than the original one and then rescales this indirect bandwidth to become a bandwidth of the original problem. The motivation for this approach comes from the observation that classical crossvalidation tends to work better when the smoothing problem is difficult. In this paper we find that the performance of indirect crossvalidation improves theoretically and practically when the polynomial order of the indirect kernel increases, with the Gaussian kernel as limiting kernel when the polynomial order goes to infinity. These theoretical and practical results support the often proposed choice of the Gaussian kernel as indirect kernel. However, for do-validation our study shows a discrepancy between asymptotic theory and practical performance. As for indirect crossvalidation, in asymptotic theory the performance of indirect do-validation improves with increasing polynomial order of the used indirect kernel. But this theoretical improvements do not carry over to practice and the original do-validation still seems to be our preferred bandwidth selector. We also consider plug-in estimation and combinations of plug-in bandwidths and crossvalidated bandwidths. These latter bandwidths do not outperform the original do-validation estimator either.

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Section: Introductionsupporting

confidence: 62%

A comparative study of new cross-validated bandwidth selectors for kernel density estimation

Mammen,

Miranda,

Nielsen

et al. 2012

Preprint

Self Cite

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“…We are currently investigating to adapt cross-validation and Do-validation to global polynomial kernel hazard estimation. This would involve generalising the cross-validation and do-validation procedures given in Gámiz Pérez et al (2013b) to also include picking the order of the adjusting polynomial. The estimation error is measured as the average over 250 simulation runs.…”

Section: Resultsmentioning

confidence: 99%

“…Recently there is a huge development in the case of filtered data, see e.g. Nielsen, Tanggaard & Jones (2009), Gámiz Pérez, Martínez Miranda & Nielsen (2013b and Spreeuw, Nielsen & Jarner (2013). The case of kernel hazard estimation is studied in Nielsen & Tanggaard (2001).…”

Section: Introductionmentioning

confidence: 99%

Global Polynomial Kernel Hazard Estimation

Hiabu

Martínez-Miranda

Nielsen

et al. 2015

Rev. colomb. estad.

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This paper introduces a new bias reducing method for kernel hazard estimation. The method is called global polynomial adjustment (GPA). It is a global correction which is applicable to any kernel hazard estimator. The estimator works well from a theoretical point of view as it asymptotically reduces bias with unchanged variance. A simulation study investigates the finite-sample properties of GPA. The method is tested on local constant and local linear estimators. From the simulation experiment we conclude that the global estimator improves the goodness-of-fit. An especially encouraging result is that the bias-correction works well for small samples, where traditional bias reduction methods have a tendency to fail.Key words: Kernel estimation; hazard function; local linear estimation; boundary kernels; polynomial correction. ResumenEn este artículo se introduce un nuevo método de correción del sesgo para la estimación núcleo de la función de riesgo. El método, denominado ajuste polinomial global (APG), consiste en una corrección global que es aplicable a cualquier tipo de estimador núcleo de la función de riesgo. Se comprueba que APG posee buenas propiedades asintóticas y que consigue reducir el sesgo sin incrementar la varianza. Se realizan estudios de simulación para evaluar las propiedades del APG en muestras finitas. Dichos estudios muestran un buen comportamiento en la práctica del APG. Esto es especialmente alentador dado que para muestras finitas los métodos tradicionales de reducción del sesgo tienden a tener un comportamiento bastante pobre.Palabras clave: Estimación kernel; funciones de riesgo; estimación local lineal; kernels de frontera, corrección polinomial.----------

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One-sided cross-validation for nonsmooth density functions

Savchuk

2019

Comput Stat

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One-sided cross-validation (OSCV) is a bandwidth selection method initially introduced by Hart and Yi (1998) in the context of smooth regression functions. Martínez-Miranda et al. (2009) developed a version of OSCV for smooth density func-tions. This article extends the method for nonsmooth densities. It also introduces the fully robust OSCV modification that produces consistent OSCV bandwidths for both smooth and nonsmooth cases. Practical implementations of the OSCV method for smooth and nonsmooth densities are discussed. One of the considered cross-validation kernels has potential for improving the OSCV method's implementation in the regression context.

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Smoothing survival densities in practice

Cited by 10 publications

References 24 publications

A comparative study of new cross-validated bandwidth selectors for kernel density estimation

A comparative study of new cross-validated bandwidth selectors for kernel density estimation

Global Polynomial Kernel Hazard Estimation

One-sided cross-validation for nonsmooth density functions

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