Strong convergence of the functional nonparametric relative error regression estimator under right censoring
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Omar Fetitah
und
Ali Righi
Abstract
In this paper, we investigate the asymptotic properties of a nonparametric estimator of the relative error regression given a functional explanatory variable, in the case of a scalar censored response, we use the mean squared relative error as a loss function to construct a nonparametric estimator of the regression operator of these functional censored data. We establish the strong almost complete convergence rate and asymptotic normality of these estimators. A simulation study is performed to illustrate and compare the higher predictive performances of our proposed method to those obtained with standard estimators.
The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through the Research Groups Program under grant number R.G.P. 2/67/41.
Acknowledgement
The authors would like to thank the anonymous reviewers for their valuable comments and suggestions which improved substantially the quality of this paper.
References
[1] Altendji, B. et al.: Functional data analysis: estimation of the relative error in functional regression under random left-truncation model, J. Nonparametr. Stat. 30 (2018), 472–490.10.1080/10485252.2018.1438609Suche in Google Scholar
[2] Attouch, M. K.—Laksaci, A.—Messabihi, N.: Nonparametric relative error regression for spatial random variables, Statist. Papers 58 (2017), 987–1008.10.1007/s00362-015-0735-6Suche in Google Scholar
[3] Campbell, M.—Donner, A.: Classification efficiency of multinomial logistic regression relative to ordinal logistic regression, J. Amer. Statist. Assoc. 84 (1989), 587–591.10.1080/01621459.1989.10478807Suche in Google Scholar
[4] Carbonez, A.—Gyorfi, L.—Edward, C.: Partitioning-estimates of a regression function under random censoring, Statist. Decisions 13 (1995), 21–38.10.1524/strm.1995.13.1.21Suche in Google Scholar
[5] Chaouch, M.—Laib, N.—Ould-Said, E.: Nonparametric M-estimation for right censored regression model with stationary ergodic data, Stat. Methodol. 33 (2016), 234–255.10.1016/j.stamet.2016.10.002Suche in Google Scholar
[6] Chen, K.—Guo, S.—Lin, Y.—Ying, Z.: Least absolute relative error estimation, J. Amer. Statist. Assoc. 105 (2010), 1104–1112.10.1198/jasa.2010.tm09307Suche in Google Scholar PubMed PubMed Central
[7] Demongeot, J. et al.: Relative-error prediction in nonparametric functional statistics: Theory and practice, J. Multivariate Anal. 147 (2016), 261–268.10.1016/j.jmva.2015.09.019Suche in Google Scholar
[8] Deheuvels, P.—Einmahl, J. H. J.: Functional limit laws for the increments of Kaplan Meier product-limit processes and applications, Ann. Probab. 28 (2000), 1301–1335.10.1214/aop/1019160336Suche in Google Scholar
[9] Feller, W.: An Introduction to Probability Theory and Its Applications Volume II, Willey Series in Probability and Mathematical Statistics, 1966.Suche in Google Scholar
[10] Ferraty, F.—Vieu, P.: Nonparametric Functional Data Analysis: Theory and Practice, Springer Series in Statistics Springer New York, 2006.Suche in Google Scholar
[11] Ferraty, F.—Mas, A.—Vieu, P.: Nonparametric regression on functional data: Inference and practical aspects, Aust. N. Z. J. Stat. 49 (2007), 267–286.10.1111/j.1467-842X.2007.00480.xSuche in Google Scholar
[12] Helal, N.—Ould-Said, E.: Kernel conditional quantile estimator under left truncation for functional regressors, Opuscula Math. 36 (2016), 25–48.10.7494/OpMath.2016.36.1.25Suche in Google Scholar
[13] Horrigue, W.—Ould-Said, E.: Strong uniform consistency of a nonparametric estimator of a conditional quantile for censored dependent data and functional regressors, Random Oper. Stoch. Equ. 19 (2011), 131–156.10.1515/ROSE.2011.008Suche in Google Scholar
[14] Horrigue, W.—Ould-Said, E.: Nonparametric regression quantile estimation for dependant functional data under random censorship: Asymptotic normality, Comm. Statist. Theory Methods 44 (2014), 4307–4332.10.1080/03610926.2013.784993Suche in Google Scholar
[15] Jones, M. et al.: Relative error prediction via kernel regression smoothers, J. Statist. Plann. Inference 138 (2008), 2887–2898.10.1016/j.jspi.2007.11.001Suche in Google Scholar
[16] Kaplan, E. L.— Meier, P.: Nonparametric estimation from incomplete observations, J. Amer. Statist. Assoc. 53 (1958), 457–481.10.1007/978-1-4612-4380-9_25Suche in Google Scholar
[17] Khardani, S.—Thiam, B.: Strong consistency result of a non parametric conditional mode estimator under random censorship for functional regressors, Comm. Statist. Theory Methods 45 (2016), 1863–1875.10.1080/03610926.2013.867997Suche in Google Scholar
[18] Khardani, S.—Lemdani, M.—Ould-Said, E.: Some asymptotic properties for a smooth kernel estimator of the conditional mode under random censorship, J. Korean Statist. Soc. 39 (2010), 455–469.10.1016/j.jkss.2009.10.001Suche in Google Scholar
[19] Khardani, S.—Lemdani, M.—Ould-Said, E.: Uniform rate of strong consistency for a smooth Kernel estimator of the conditional mode under random censorship, J. Statist. Plann. Inference 141 (2011), 3426–3436.10.1016/j.jspi.2011.04.023Suche in Google Scholar
[20] Köhler, M.—Máthé, K.—Pintér, M.: Prediction from randomly right censored data, J. Multivariate Anal. 80 (2002), 73–100.10.1006/jmva.2000.1973Suche in Google Scholar
[21] Loéve, M.: Pobability Theory, 3rd Ed. Van Nostrand Princeton, 1963.Suche in Google Scholar
[22] Ould-Said, E.—Guessoum, Z.: On nonparametric estimation of the regression function under random censorship model, Statist. Decisions 26 (2008), 159–177.10.1524/stnd.2008.0919Suche in Google Scholar
[23] Ramsay, J.— Silverman, B. W.: Functional Data Analysis, Springer Series in Statistics, Springer-Verlag New York, 2005.10.1007/b98888Suche in Google Scholar
[24] Thiam, B.: Relative error prediction in nonparametric deconvolution regression model, Stat. Neerl. 10 (2018), 1–15.10.1111/stan.12135Suche in Google Scholar
[25] Ruiz-Velasco, S.: Asymptotic efficiency of logistic regression relative to linear discriminant analysis, Biometrika 78 (1991), 235–243.10.1093/biomet/78.2.235Suche in Google Scholar
© 2020 Mathematical Institute Slovak Academy of Sciences
Artikel in diesem Heft
- Regular papers
- Fuzzy deductive systems of RM algebras
- Congruence pairs of principal MS-algebras and perfect extensions
- The lattices of 𝔏-fuzzy state filters in state residuated lattices
- Central lifting property for orthomodular lattices
- EQ-Modules
- On the exponential Diophantine equation Pxn + Pxn+1 + ⋯ + Pxn+k-1 = Pm
- Remarks on some generalization of the notion of microscopic sets
- Disjointness of composition operators on Hv0 spaces
- A common fixed point theorem for non-self mappings in strictly convex menger PM-spaces
- The Poincaré-Cartan forms of one-dimensional variational integrals
- Coarse cohomology with twisted coefficients
- Divisible extension of probability
- Asymptotic behavior of the records of multivariate random sequences in a norm sense
- Strong convergence of the functional nonparametric relative error regression estimator under right censoring
- A new kumaraswamy generalized family of distributions: Properties and applications
- Efficient message transmission via twisted Edwards curves
- Computation of several Hessenberg determinants
Artikel in diesem Heft
- Regular papers
- Fuzzy deductive systems of RM algebras
- Congruence pairs of principal MS-algebras and perfect extensions
- The lattices of 𝔏-fuzzy state filters in state residuated lattices
- Central lifting property for orthomodular lattices
- EQ-Modules
- On the exponential Diophantine equation Pxn + Pxn+1 + ⋯ + Pxn+k-1 = Pm
- Remarks on some generalization of the notion of microscopic sets
- Disjointness of composition operators on Hv0 spaces
- A common fixed point theorem for non-self mappings in strictly convex menger PM-spaces
- The Poincaré-Cartan forms of one-dimensional variational integrals
- Coarse cohomology with twisted coefficients
- Divisible extension of probability
- Asymptotic behavior of the records of multivariate random sequences in a norm sense
- Strong convergence of the functional nonparametric relative error regression estimator under right censoring
- A new kumaraswamy generalized family of distributions: Properties and applications
- Efficient message transmission via twisted Edwards curves
- Computation of several Hessenberg determinants
