journal article
Open Access
Feb 04, 2024
A Comprehensive Analysis of MSE in Estimating Conditional Hazard Functions: A Local Linear, Single Index Approach for MAR Scenarios
Abstract
In unveiling the non-parametric estimation of the conditional hazard function through the local linear method, our study yields key insights into the method’s behavior. We present rigorous analyses demonstrating the mean square convergence of the estimator, subject to specific conditions, within the realm of independent observations with missing data. Furthermore, our contributions extend to the derivation of expressions detailing both bias and variance of the estimator. Emphasizing the practical implications, we underscore the applicability of two distinct models discussed in this paper for single index estimation scenarios. These findings not only enhance our understanding of survival analysis methodologies but also provide practitioners with valuable tools for navigating the complexities of missing data in the estimation of conditional hazard functions. Ultimately, our results affirm the robustness of the local linear method in non-parametrically estimating the conditional hazard function, offering a nuanced perspective on its performance in the challenging context of independent observations with missing data.
Topics
No keywords indexed for this article. Browse by subject →
References
32
[1]
Attaoui "Strong uniform consistency rates and asymptotic normality of conditional density estimator in the single functional index modeling for time series data" Adv. Stat. Anal. (2014) 10.1007/s10182-014-0227-3
[2]
Baillo "Local linear regression for functional predictor and scalar response" J. Multivar. Anal. (2009) 10.1016/j.jmva.2008.03.008
[3]
Ferraty "Locally modelled regression and functional data" J. Nonparametric Stat. (2010) 10.1080/10485250903089930
[4]
Berlinet "Local linear regression for functional data" Ann. Inst. Stat. Math. (2011) 10.1007/s10463-010-0275-8
[5]
Bouchentouf "Strong uniform consistency rates of some characteristics of the conditional distribution estimator in the functional single-index model" Appl. Math. (2014)
[6]
Benchiha "Local linear estimate for functional regression with missing data at random" Int. J. Math. Stat. (2018)
[7]
Cheng "Nonparametric estimation of mean functionals with data missing at random" J. Am. Stat. Assoc. (1994) 10.1080/01621459.1994.10476448
[8]
Demongeot "Local linear estimation of the conditional density for functional data" Comptes Rendus Math. (2010) 10.1016/j.crma.2010.06.013
[9]
Fan, J., and Gijbels, I. (1996). Local Polynomial Modelling and Its Applications, Chapman and Hall/CRC. Monographs on Statistics and Applied Probability 66.
[10]
Fan, J., and Yao, Q. (2003). Non Linear Time Series. Nonparametric and Parametric Methods, Springer.
10.1007/b97702
[11]
Ferraty, F., and Vieu, P. (2003). Nonparametric Functional Data Analysis, Springer.
[12]
Ferraty "Non-paramétrique regression on functional data: Infernce and practical aspects" Aust. N. Z. J. Stat. (2007) 10.1111/j.1467-842x.2007.00480.x
[13]
Ferraty, F., Park, J., and Vieu, P. (2011). Recent Advances in Functional Data Analysis and Related Topics, Contribution to Statistics, Physica, Physica-Verlag HD.
10.1007/978-3-7908-2736-1
[14]
Little, R.J.A., and Rubin, D.B. (2002). Statistical Analysis with Missing Data, John Wiley & Sons, Inc.
10.1002/9781119013563
[15]
Boj "Distance-based local linear regression for functional predictors" Comput. Stat. Data Anal. (2010) 10.1016/j.csda.2009.09.010
[16]
Belabbaci "Strong Uniform Consistency of Hazard Function with Functional Explicatory Variable in Single Functional Index Model under Censored Data" Appl. Appl. Math. Int. J. (AAM) (2015)
[17]
Bouiadjra "Conditional hazard function estimate for functional data with missing at random" Int. J. Stat. Econ. (2017)
[18]
Rachdi "Local weighted average estimation of the regression operator for functional data" Commun. Stat.-Theory Methods (2011) 10.1080/03610921003778209
[19]
Efromovich "Nonparametric regression with responses missing at random" J. Stat. Plan. Inference (2011) 10.1016/j.jspi.2011.06.017
[20]
Ferraty "Modèle à indice fonctionnel simple" C. R. Acad. Sci. Paris (2003) 10.1016/s1631-073x(03)00239-5
[21]
Ferraty "Mean estimation with data missing at random for functional covariables" Statistics (2013) 10.1080/02331888.2011.650172
[22]
Fetitah "Mean estimation with data missing at random for functional covariables" Metrika (2023) 10.1007/s00184-023-00898-1
[23]
Hamidi "Estimation of the Conditional Quantile for Functional Stationary Ergodic Data with Responses Missing at Random" J. Probab. Stat. Sci. (2018)
[24]
Kenouza "Functional local linear estimate of the conditional hazard function with missing at random" Int. J. Appl. Math. Stat. (2019)
[25]
Kadiri "Strong uniform consistency rates of conditional quantile estimation in the single functional index model under random censorship" Depend. Model. (2018) 10.1515/demo-2018-0013
[26]
Ling "Nonparametric regression estimation for functional stationary ergodic data with missing at random" J. Stat. Plan. Inference (2015) 10.1016/j.jspi.2015.02.001
[27]
Ling "Conditional mode estimation for functional stationary ergodic data with responses missing at random" Statistics (2016) 10.1080/02331888.2015.1122012
[28]
Roussas "Hazard rate estimation under dependence conditions" J. Stat. Plan. Inference (1989) 10.1016/0378-3758(89)90067-0
[29]
Demongeot "On the Local Linear Modelization of the Conditional Distribution for Functional Data" Sankhya A (2014) 10.1007/s13171-013-0050-z
[30]
Rachdi "Theoretical and practical aspects of the quadratic error in the local linear estimation of the conditional density for functional data" Comput. Stat. Data Anal. (2014) 10.1016/j.csda.2013.11.011
[31]
Merouan "Quadratic error of the conditional hazard function in the local linear estimation for functional data" Int. J. Afr. Stat. (2018)
[32]
Tabti "Estimation and simulation of conditional hazard function in the quasi-associated framework when the observations are linked via a functional single-index structure" Commu. Stat. Theory Methods (2018) 10.1080/03610926.2016.1213294
Metrics
2
Citations
32
References
Details
- Published
- Feb 04, 2024
- Vol/Issue
- 12(3)
- Pages
- 495
- License
- View
Authors
Funding
King Khalid University
Award: PNURSP2024R358
Princess Nourah bint Abdulrahman University
Award: PNURSP2024R358
Cite This Article
Abderrahmane Belguerna, Hamza Daoudi, Khadidja Abdelhak, et al. (2024). A Comprehensive Analysis of MSE in Estimating Conditional Hazard Functions: A Local Linear, Single Index Approach for MAR Scenarios. Mathematics, 12(3), 495. https://doi.org/10.3390/math12030495
Related
You May Also Like
Mitigating the Multicollinearity Problem and Its Machine Learning Approach: A Review
Jireh Yi-Le Chan, Steven Mun Hong Leow · 2022
463 citations
Numerical Solution of Fractional Differential Equations: A Survey and a Software Tutorial
Roberto Garrappa · 2018
418 citations
Survey on Synthetic Data Generation, Evaluation Methods and GANs
Alvaro Figueira, Bruno Vaz · 2022
344 citations
Roles and Research Trends of Artificial Intelligence in Mathematics Education: A Bibliometric Mapping Analysis and Systematic Review
Gwo-Jen Hwang, Yun-Fang Tu · 2021
271 citations
Auto-Encoders in Deep Learning—A Review with New Perspectives
Shuangshuang Chen, Wei Guo · 2023
265 citations