Nonparametric density and survival function estimation in the multiplicative censoring model

Elodie Brunel (), Fabienne Comte () and Valentine Genon-Catalot ()
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Elodie Brunel: Université Montpellier, I3M UMR CNRS 5149
Fabienne Comte: Université Paris Descartes, MAP5, UMR CNRS 8145
Valentine Genon-Catalot: Université Paris Descartes, MAP5, UMR CNRS 8145

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2016, vol. 25, issue 3, No 9, 570-590

Abstract: Abstract Consider the multiplicative censoring model given by $$Y_i=X_iU_i$$ Y i = X i U i , $$i=1, \ldots ,n$$ i = 1 , … , n where $$(X_i)$$ ( X i ) are i.i.d. with unknown density f on $${\mathbb {R}}$$ R , $$(U_i)$$ ( U i ) are i.i.d. with uniform distribution $${\mathcal {U}}([0,1])$$ U ( [ 0 , 1 ] ) and $$(U_i)$$ ( U i ) and $$(X_i)$$ ( X i ) are independent sequences. Only the sample $$(Y_i)$$ ( Y i ) is observed. We study nonparametric estimators of both the density f and the corresponding survival function $$\bar{F}$$ F ¯ . First, kernel estimators are built. Pointwise risk bounds for the quadratic risk are given, and upper and lower bounds for the rates in this setting are provided. Then, in a global setting, a data-driven bandwidth selection procedure is proposed. The resulting estimator has been proved to be adaptive in the sense that its risk automatically realizes the bias-variance compromise. Second, when the $$X_i$$ X i s are nonnegative, using kernels fitted for $${\mathbb {R}}^+$$ R + -supported functions, we propose new estimators of the survival function which are also adaptive. By simulation experiments, we check the good performances of the estimators and compare the two strategies.

Keywords: Adaptive procedure; Bandwidth selection; Kernel estimators; Multiplicative censoring model; 62G07; 62N01 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11749-016-0479-1

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