Local linear approach: conditional density estimate for functional and censored data

• Autorzy: Benkhaled Abdelkader , Madani Fethi

Identyfikatory

DOI

10.1515/dema-2022-0018

• Języki publikacji: EN

Abstrakty

EN

Let Y be a random real response, which is subject to right censoring by another random variable C . In this paper, we study the nonparametric local linear estimation of the conditional density of a scalar response variable and when the covariable takes values in a semi-metric space. Our main aim is to prove under some regularity conditions both the pointwise and the uniform almost-sure consistencies with convergence rates of the conditional density estimator related by this estimation procedure.

Słowa kluczowe

EN

functional data; local linear estimator; conditional density; small-ball probability; censored data

PL

estymator liniowy; gęstość warunkowa; dane cenzurowane

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2022
• Tom: Vol. 55, nr 1
• Strony: 315--327
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Benkhaled Abdelkader

• Department of Biology, University of Mascara, Laboratory of Stochastic Models, Statistics and Applications, University Tahar Moulay of Saida, Mascara, 29000, Algeria

autor

Madani Fethi

• University Tahar Moulay of Saida, Laboratory of Stochastic Models, Statistic and Applications, Saida, 20000, Algeria

Bibliografia

• [1] J. Demongeot, A. Laksaci, F. Madani, and M. Rachdi, Functional data: local linear estimation of the conditional density and its application, Statistics 47 (2013), no. 1, 26–44, DOI: https://doi.org/10.1080/02331888.2011.568117.
• [2] M. Rachdi, A. Laksaci, J. Demongeot, A. Abdali, and F. Madani, Theoretical and practical aspects of the quadratic error in the local linear estimation of the conditional density for functional data, Comput. Statist. Data Anal. 73 (2014), 53–68, DOI: https://doi.org/10.1016/j.csda.2013.11.011.
• [3] X. Xiong, P. Zhou, and C. Ailian, Asymptotic normality of the local linear estimation of the conditional density for functional time series data, Comm. Statist. Theory Methods 47 (2018), no. 14, 3418–3440, DOI: https://doi.org/10.1080/03610926.2017.1359292.
• [4] F. Messaci, N. Nemouchi, I. Ouassou, and M. Rachdi, Local polynomial modeling of the conditional quantile for functional data, Stat. Methods Appl. 24 (2015), no. 4, 597–622, DOI: https://doi.org/10.1007/s10260-015-0296-9.
• [5] A. Benkhaled, F. Madani, and S. Khardani, Strong consistency of local linear estimation of a conditional density function under random censorship, Arab. J. Math. 9 (2020), no. 3, 513–529, DOI: https://doi.org/10.1007/s40065-020-00282-1.
• [6] A. Benkhaled, F. Madani, and S. Khardani, Asymptotic normality of the local linear estimation of the conditional density for functional dependent and censored data, South African Statist. J. 54 (2020), no. 2, 131–151, DOI: https://doi.org/10.37920/sasj.2020.54.2.1.
• [7] J. Barrientos-Marin, F. Ferraty, and P. Vieu, Locally modeled regression and functional data, J. Nonparametr. Stat. 22 (2009), no. 3, 617–632, DOI: https://doi.org/10.1080/10485250903089930.
• [8] J. Barrientos-Marin, Some Practical Problems of Recent Nonparametric Procedures: Testing, Estimation, and Application, PhD thesis (in French), Paul Sabatier’s University, Toulouse, 2007.
• [9] P. Deheuvels and H. Einmahl, Functional limit laws for the increments of Kaplan-Meier product limit processes and applications, Ann. Probab. 28 (2000), no. 3, 1301–1335, DOI: https://doi.org/10.1214/aop/1019160336.
• [10] P. Sarda and P. Vieu, Kernel Regression, Wiley, New York, 2000, pp. 43–70.
• [11] F. Ferraty and P. Vieu, Nonparametric Functional Data Analysis. Theory and Practice, Springer Series in Statistics, New York, 2006.
• [12] F. Ferraty, A. Laksaci, A. Tadj, and P. Vieu, Rate of uniform consistency for nonparametric estimates with functional variables, Inference 140 (2010), no. 2, 335–352, DOI: https://doi.org/10.1016/j.jspi.2009.07.019.

Uwagi

PL

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).