Mean square error of the estimator of the conditional hazard function

Rabhi, Abbes; Benaissa, Samir; Hamel, El Hadj; Mechab, Boubaker

doi:10.4064/am40-4-2

Cited by 3 publications

(7 citation statements)

References 8 publications

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“…We point out that our asymptotic results are useful in some statistical problems such as the choice of the smoothing parameters, the determination of confidence intervals and in risk analysis. The present work extended to dependent case the result of Rabhi et al [21] given in i.i.d. case functional.…”

Section: Introductionsupporting

confidence: 54%

“…They give the rates of convergence (in an almost complete sense) to the corresponding functions, in an a dependence (α-mixing) context. In Rabhi et al [21], the same properties are shown in an i.i.d. context in the data sample.…”

Section: Introductionmentioning

confidence: 56%

“…By using the same decomposition used in ( Theorem 3.1 Rabhi et al [21], P.408), we show that the proof of Theorem 3.1 can be deduced from the following intermediates results:…”

Section: Theorem 31 Under Assumptions (H0)-(h6) We Havementioning

confidence: 89%

“…case and under α-mixing condition . Recently, Rabhi et al [21] studied the mean quadratic convergence in the i.i.d. case of this estimate.…”

Section: Introductionmentioning

confidence: 99%

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Conditional risk estimate for functional data under strong mixing conditions

Rabhi¹,

Soltani²,

Traore³

2015

JSTA

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We consider the problem of nonparametric estimation of the conditional hazard function for functional mixing data. More precisely, given a strictly stationary random variables Z i = (X i , Y i ) i∈N , we investigate a kernel estimate of the conditional hazard function of univariate response variable Y i given the functional variable X i . The principal aim of this paper is to give the mean squared convergence rate and to prove the asymptotic normality of the proposed estimator.

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Section: Introductionsupporting

confidence: 54%

Section: Introductionmentioning

confidence: 56%

“…By using the same decomposition used in ( Theorem 3.1 Rabhi et al [21], P.408), we show that the proof of Theorem 3.1 can be deduced from the following intermediates results:…”

Section: Theorem 31 Under Assumptions (H0)-(h6) We Havementioning

confidence: 89%

“…case and under α-mixing condition . Recently, Rabhi et al [21] studied the mean quadratic convergence in the i.i.d. case of this estimate.…”

Section: Introductionmentioning

confidence: 99%

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Conditional risk estimate for functional data under strong mixing conditions

Rabhi¹,

Soltani²,

Traore³

2015

JSTA

Self Cite

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show abstract

“…They calculated the bias and variance of these estimates, and established their asymptotic normality. Still while using the Kernel method, Rabhi et al (2013) determined the asymptotic mean square error of the proposed estimator of the conditional hazard function. In the nonfunctional case, a short overview on nonparametric conditional hazard function estimation can be found in Spierdijk (2008).…”

Section: Introductionmentioning

confidence: 99%

Quadratic error of the conditional hazard function in the local linear estimation for functional data

Merouan¹,

Mechab²,

Massim³

2018

JAS

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In this paper we investigate the asymptotic mean square error and the rates of convergence of the estimator based on the local linear method of the conditional hazard function. Under some general conditions, the expressions of the bias and variance are given. The efficiency of our estimator is evaluated through a simulation study. We proved, theoretically and on the scope of a simulation study, that our proposed estimator has better performance than the estimator based on the standard kernel method.

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Limit Law of the Local Linear Estimate of the Conditional Hazard Function for Functional Data

Bouanani¹,

Guendouzi²,

Chemikh³

2020

Preprint

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In this work, we treat a prediction problem via the conditional hazard function of a scalar response variable Y given a functional random variable X by using the local linear technique. The main purpose of this paper is to investigate the asymptotic normality of the nonparametric estimator of the conditional hazard function, under some general conditions. A simulation study, conducted to assess finite sample behavior, demonstrates the superiority of our method than the standard kernel method

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Mean square error of the estimator of the conditional hazard function

Abstract: This paper deals with a scalar response conditioned by a functional random variable. The main goal is to estimate the conditional hazard function. An asymptotic formula for the mean square error of this estimator is calculated considering as usual the bias and variance.

Cited by 3 publications

References 8 publications

Conditional risk estimate for functional data under strong mixing conditions

Conditional risk estimate for functional data under strong mixing conditions

Quadratic error of the conditional hazard function in the local linear estimation for functional data

Limit Law of the Local Linear Estimate of the Conditional Hazard Function for Functional Data

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