Nonparametric estimation of density under bias and multiplicative censoring via wavelet methods

Abbaszadeh, Mahsa; Chesneau, Christophe; Doosti, Hassan

doi:10.1016/j.spl.2012.01.016

Cited by 14 publications

(15 citation statements)

References 19 publications

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“…For (4), by (2), yf Y (y) tends to 0 as both y tends to +∞ and −∞. By (3), EY 2 (t (Y )) 2 is finite.…”

Section: Proof Of Equationsmentioning

confidence: 97%

“…They obtain rates comparable to ours though on different regularity spaces, however their procedure is not adaptive and depends on the choice of a cutoff which is only empirically studied. Later on, wavelet methods have been applied by Abbaszadeh et al (2012Abbaszadeh et al ( ,2013 to estimate the density and its derivatives, considering a general L p -risk, and in presence of additional bias. Their estimators are adaptive and reach the same rates as ours up to logarithmic terms (when p = 2).…”

Section: Introductionmentioning

confidence: 99%

“…. ) rely on relationships between the density f Y and survival functionF Y = 1 − F Y of Y i and those of X i , given by (2) ∀y ∈ R, f Y (y) =…”

Section: Introductionmentioning

confidence: 99%

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Nonparametric density and survival function estimation in the multiplicative censoring model

Brunel

Comte

Genon-Catalot

2016

TEST

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Abstract. In this paper, we consider the multiplicative censoring model, given by Yi = XiUi where (Xi) are i.i.d. with unknown density f on R, (Ui) are i.i.d. with uniform distribution U([0, 1]) and (Ui) and (Xi) are independent sequences. Only the sample (Yi) 1≤i≤n is observed. Nonparametric estimators of both the density f and the corresponding survival functionF are proposed and studied. First, classical kernels are used and the estimators are studied from several points of view: pointwise risk bounds for the quadratic risk are given, upper and lower bounds for the rates in this setting are provided. Then, an adaptive non asymptotic bandwidth selection procedure in a global setting is proved to realize the bias-variance compromise in an automatic way. When the Xi's are nonnegative, using kernels fitted for R + -supported functions, we propose new estimators of the survival function which are proved to be adaptive. Simulation experiments allow us to check the good performances of the estimators and compare the two strategies.

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“…For (4), by (2), yf Y (y) tends to 0 as both y tends to +∞ and −∞. By (3), EY 2 (t (Y )) 2 is finite.…”

Section: Proof Of Equationsmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

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Nonparametric density and survival function estimation in the multiplicative censoring model

Brunel

Comte

Genon-Catalot

2016

TEST

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“…The inverse problems considered here are the following ones. First, we assume that observations are (1) Y i = X i U i , i = 1, . .…”

Section: Introductionmentioning

confidence: 99%

“…Vardi (1989)). Numerous papers deal with the estimation of f for model (1) whether by nonparametric maximum likelihood (Vardi (1989), Vardi and Zhang (1992), Asgharian et al (2012)), by projection methods (Andersen and Hansen (2001), Abbaszadeh et al (2012Abbaszadeh et al ( ,2013) or kernel methods (Brunel et al (2015)). In Belomestny et al (2016), f is supposed to be R + -supported and estimated by projection estimators on a Laguerre basis.…”

Section: Introductionmentioning

confidence: 99%

Laguerre and Hermite bases for inverse problems

Comte

Genon-Catalot

2018

Journal of the Korean Statistical Society

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Abstract. We present inverse problems of nonparametric statistics which have a performing and smart solution using projection estimators on bases of functions with non compact support, namely, a Laguerre basis or a Hermite basis. The models are Yi = XiUi, Zi = Xi + Σi, where the Xi's are i.i.d. with unknown density f , the Σi's are i.i.d. with known density fΣ, the Ui's are i.i.d. with uniform density on [0, 1]. The sequences (Xi), (Ui), (Σi) are independent. We define projection estimators of f in the two cases of indirect observations of (X1, . . . , Xn), and we give upper bounds for their L 2 -risks on specific Sobolev-Laguerre or Sobolev-Hermite spaces. Data-driven procedures are described and proved to perform automatically the bias variance compromise.

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Wavelet estimations for mixed densities under multiplicative censoring

Cao

Wang

Zeng

2019

Math Methods in App Sciences

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Using compactly supported wavelets, Chaubey et al consider L2‐risk estimation for mixed density under multiplicative censoring (Chaubey YP, Chesneau C, Doosti H. Adaptive wavelet estimation of a density from mixtures under multiplicative censoring. Statistics, 2015, 49: 638‐659). In this paper, we try to discuss Lp‐risk (1 ≤ p<∞) estimation for that statistical model of the linear and nonlinear wavelet estimators respectively. Our results can be seen as an extension of the work of Chaubey et al.

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Nonparametric estimation of density under bias and multiplicative censoring via wavelet methods

Cited by 14 publications

References 19 publications

Nonparametric density and survival function estimation in the multiplicative censoring model

Nonparametric density and survival function estimation in the multiplicative censoring model

Laguerre and Hermite bases for inverse problems

Wavelet estimations for mixed densities under multiplicative censoring

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