Histogram selection for possibly censored data

Akakpo, Nathalie; Durot, Cécile

doi:10.3103/s1066530710030014

Cited by 6 publications

(7 citation statements)

References 21 publications

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“…Cumulative distribution function estimation in presence of measurement error is considered by DATTNER et al (). On the other hand, nonparametric or hazard rate estimation for right censored data has been studied in ANTONIADIS et al (), LI () (wavelets), DOHLER and RUSCHENDORF () (penalized likelihood‐based criterion), BRUNEL AND COMTE (), REYNAUD‐BOURET (), AKAKPO and DUROT () (penalized contrast estimators).…”

Section: Introductionmentioning

confidence: 99%

“…Cumulative distribution function estimation in presence of measurement error is considered by Dattner et al (2011). On the other hand, nonparametric or hazard rate estimation for right censored data has been studied in Antoniadis et al (1999), Li (2007Li ( , 2008 (wavelets), Dohler and Ruschendorf (2002) (penalized likelihood-based criterion), Comte (2005, 2008), Reynaud-Bouret (2006), Akakpo and Durot (2010) (penalized contrast estimators).…”

Section: Introductionmentioning

confidence: 99%

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Spline regression for hazard rate estimation when data are censored and measured with error

Comte

Mabon

Samson

2017

Statistica Neerlandica

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International audienceIn this paper, we study an estimation problem where the variables of interest are subject to both right censoring and measurement error. In this context, we propose a nonparametric estimation strategy of the hazard rate, based on a regression contrast minimized in a finite dimensional functional space generated by splines bases. We prove a risk bound of the estimator in term of integrated mean square error, discuss the rate of convergence when the dimension of the projection space is adequately chosen. Then, we define a data driven criterion of model selection and prove that the resulting estimator performs an adequate compromise. The method is illustrated via simulation experiments which prove that the strategy is successful

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Spline regression for hazard rate estimation when data are censored and measured with error

Comte

Mabon

Samson

2017

Statistica Neerlandica

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“…This model has been studied by Tanner & Wong (), Patil () and Müller & Wang (), among all. Adaptive results are available for projection‐type estimators (see Brunel & Comte, ; Reynaud‐Bouret, ; or Akakpo & Durot, ) but, to our knowledge, not for kernel ones.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Warped Kernel Estimators

Chagny

2014

Scandinavian J Statistics

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In this work, we develop a method of adaptive non‐parametric estimation, based on ‘warped’ kernels. The aim is to estimate a real‐valued function s from a sample of random couples (X,Y). We deal with transformed data (Φ(X),Y), with Φ a one‐to‐one function, to build a collection of kernel estimators. The data‐driven bandwidth selection is performed with a method inspired by Goldenshluger and Lepski (Ann. Statist., 39, 2011, 1608). The method permits to handle various problems such as additive and multiplicative regression, conditional density estimation, hazard rate estimation based on randomly right‐censored data, and cumulative distribution function estimation from current‐status data. The interest is threefold. First, the squared‐bias/variance trade‐off is automatically realized. Next, non‐asymptotic risk bounds are derived. Lastly, the estimator is easily computed, thanks to its simple expression: a short simulation study is presented.

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“…However, non-asymptotic studies seem to be rather scarce. We refer to [BC05,RB06,BC08,Pla11,AD10] for results concerning procedures based on (penalized) L 2 contrasts. We may cite [vdG95,DR02] for a study of non-asymptotic properties of maximum likelihood estimators.…”

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confidence: 99%

“…Statistical setting and notations. In this paper, the target s 0 is viewed as the intensity of a random measure ( [BB09,AD10,Bar11]). This makes possible a unified treatment of the three frameworks.…”

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confidence: 99%

Estimating a density, a hazard rate, and a transition intensity via the ρ-estimation method

Sart

2021

Ann. Inst. H. Poincaré Probab. Statist.

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We propose a unified study of three statistical settings by widening the ρ-estimation method developed in [BBS17]. More specifically, we aim at estimating a density, a hazard rate (from censored data), and a transition intensity of a time inhomogeneous Markov process. We show nonasymptotic risk bounds for an Hellinger-type loss when the models consist, for instance, of piecewise polynomial functions, multimodal functions, or functions whose square root is piecewise convexconcave. Under convex-type assumptions on the models, maximum likelihood estimators coincide with ρ-estimators, and satisfy therefore our risk bounds. However, our results also apply to some models where the maximum likelihood method does not work. Subsequently, we present an alternative way, based on estimator selection, to define a piecewise polynomial estimator. We control the risk of the estimator and carry out some numerical simulations to compare our approach with a more classical one based on maximum likelihood only.

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Histogram selection for possibly censored data

Cited by 6 publications

References 21 publications

Spline regression for hazard rate estimation when data are censored and measured with error

Spline regression for hazard rate estimation when data are censored and measured with error

Adaptive Warped Kernel Estimators

Estimating a density, a hazard rate, and a transition intensity via the ρ-estimation method

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