Oussama Bouanani, Mustapha Mohammedi

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This research study the k-Nearest Neighbors (k-NN) of the conditional mode by using the local linear technique in the case of a scalar response variable that are linked via a single-index structure. The main contribution of this work is to investigate the asymptotic normality of the nonparametric estimator of the conditional mode under some general assumptions. A simulation study was conducted to assess finite sample behavior to exhibit the eectiveness of our method over the standard kernel method.


Local constant estimator, Local linear estimation, Asymptotic normality, Conditional mode, Functional data, $k$-Nearest Neighbors ($k$-NN), Single functional index model

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bibitem{12}{sc A. Ait-Sa"{i}di, F. Ferraty, R. Kassa, {rm and} P. Vieu}: textit{Cross-validated estimations in the single-functional index model.} Statistics . textbf{42}, (2008), 475-494.

bibitem{sss1}{ sc I. Almanjahie, Z. Kaid, A. Laksaci, {rm and} M. Rachdi}:textit{ Predicting temperature curve based on fast kNN local linear estimation of the conditional distribution function}. PeerJ . textbf{9},(2021), pp. e11719 .

bibitem{d2021} {sc I. Almanjahie, W. Alahmari, A. Laksaci, {rm and} M. Rachdi}: textit{Computational aspects of the k NN local linear smoothing for some conditional models in high dimensional statistics.} Communications In Statistics-Simulation And Computation. (2021), pp. 1-32.

bibitem{d2022}{ sc I. Almanjahie, K. A . Assiri, A. Laksaci, Z. Chikr Elmezouar} textit{ The k nearest neighbors smoothing of the relative-error regression with functional regressor,} Commun. Stat. Theory Methods, textbf{51}. (2022), 4196–4209.

bibitem {d20222} { sc İ. Almanjahie , W. Mesfer and L. Ali }, textit{ The k nearest neighbors local linear estimator of functional conditional density when there are missing data}, Hacettepe Journal of Mathematics and Statistics, textbf{ 51} , (2022) no. 3, pp. 914-931.

bibitem{alshahrani2023knn} { sc F. Alshahrani, W. Bouabsa, I. Almanjahie {rm and} M. Kadi, } textit{ kNN local linear estimation of the conditional density and mode for functional spatial high dimensional data.} AIMS Mathematics. textbf{8}, (2023), 15844-15875.

bibitem{Ab}{sc S. Attaoui, {rm and} N. Ling} : textit{Asymptotic results of a nonparametric conditional cumulative distribution estimator in the single functional index modeling for time series data with applications}. Metrika. textbf{79}, (2016), 485-511.

bibitem{AB12}{sc M. Attouch {rm and} B. Tawfik}: textit{Asymptotic distribution of robust k-nearest neighbour estimator for functional nonparametric models}. Matematichki Vesnik. textbf{64}, (2012), 275-285.

bibitem{bo} {sc O. Bouanani, A. Laksaci, M. Rachdi {rm and} S. Rahmani} : textit{Asymptotic normality of some conditional nonparametric functional parameters in high-dimensional statistics}. Behaviormetrika. textbf{46} ,(2019), pp. 199-233.

bibitem{booo} {sc O. Bouanani, S. Rahmani, A. Laksaci, {rm and}M. Rachdi }:textit{ Asymptotic normality of conditional mode estimation for functional dependent data}. Indian Journal Of Pure And Applied Mathematics . textbf{51}, (2020), 465-481.

bibitem{3} {sc D. Bosq}textit{ Linear processes in function spaces: theory and applications}. (Springer Science and Business Media, (2000).

bibitem{k1} {sc F. Burba, F. Ferraty {rm and} P. Vieu} textit{k-Nearest Neighbour method in functional nonparametric regression.} Journal Of Nonparametric Statistics. textbf{21}, (2009), 453-469.

bibitem{CA06} {sc F. C'{e}rou, {rm and} A. Guyader}: textit{Nearest neighbor classification in infinite dimension}. ESAIM: PS. textbf{10}, (2006), pp. 340-355.

bibitem{d1d} {sc Z. Chikr-Elmezouar, I.M. Almanjahie, A. Laksaci {rm and} M. Rachdi}:textit{ FDA: strong consistency of the kNN local linear estimation of the functional conditional density and mode}. Journal of Nonparametric Statistics. textbf{31}(1), (2019), 175-195.

bibitem{C80} {sc G. Collomb}: textit{ Estimation de la r'{e}gression par la m'{e}thode des k points les plus proches avec noyau: quelques propri'{e}t'{e}s de convergence ponctuelle}. Nonparametric Asymptotic Statistics (Proc. Conf., Rouen, 1979) (French). textbf{821}, (1980), pp. 159-175.

bibitem{Dabo12H} {sc S. Dabo-Niang, Z. Kaid, {rm and} A. Laksaci} textit{ On spatial conditional mode estimation for a functional regressor}. Statist. Probab. Lett. , {bf 82},(2012), 1413-1421.

bibitem{Demongeot11} {sc J. Demongeot, A. Laksaci , F. Madani, {rm and} M. Rachdi}: textit{Functional data: local linear estimation of the conditional density and its application,} textit{ Statistics.} {bf47}, (2013), 26-44.

bibitem{1} {sc J. Dauxois, A. Pousse, {rm and} Y. Romain}: textit{Asymptotic theory for the principal component analysis of a vector random function: some applications to statistical inference}. Journal Of Multivariate Analysis . textbf{12},(1982), 136-154.

bibitem{F} {sc J. Fan}: textit{Local Polynomial Modelling and Its Applications}. Pub. Location Boca Raton, 1996.

bibitem{101} {sc J. Fan, {rm and} I. Gijbels}textit{ Local polynomial modelling and its applications: monographs on statistics and applied probability} 66. (Routledge,2018).

bibitem{10}{sc F. Ferraty, A. Peuch, {rm and} P. Vieu}: textit{Modèle à indice fonctionnel simple}. Comptes Rendus Mathematique. textbf{336}, (2003), 1025-1028

bibitem{FLV05H}{sc F. Ferraty, A. Laksaci, {rm and} F. Vieu}: textit{ Functional time series

prediction via the conditional mode estimation.} C. R., Math., Acad. Sci. Paris, {bf 340}, (2005), 389-392.

bibitem{Fes} {sc F. Ferraty {rm and } P. Vieu}. textit{ Nonparametric functional data analysis}. Springer, New York, Theory and practice, 2006

bibitem{15} {sc A. Goia, {rm and} P. Vieu,} textit{A partitioned single functional index model}. Computational Statistics. textbf{30}, (2015), 673-692

bibitem{KLOH} {sc S. Khardani, M. Lemdani, {rm and} E. Ould-Sa"{i}d}: textit{Uniform rate of

strong consistency for a smooth kernel estimator of the conditional

mode for censored time series}. J. Statist. Plann. Inference , {bf 141}, (2011), 3426-3436.

bibitem{R}{sc M. Rachdi, A. Laksaci, J. Demongeot, A. Abdali {rm and} F. Madani} textit{Theoretical and practical aspects of the quadratic error in the local linear estimation of the conditional density for functional data}. Comput. Stat. Data Anal. textbf{73},(2014), pp. 53-68.

bibitem{OT11H} { sc E. Ould-Sa"{i}d and Tatachak, A.} A nonparametric conditional mode estimate under RLT model and strong mixing condition. {em Int. J. Stat. Econ.}, {bf 6}, 76-92. (2011)

bibitem{L} {sc A. Laksaci, F. Madani {rm and} M. Rachdi}: textit{Kernel conditional density estimation when the regressor is valued in a semi-metric space}. Communcations in Statistics-Theory and Methods. textbf{42}(19),( 2013), 3544-3570.

bibitem{102} {sc A. Laksaci, M. Rachdi {rm and} S. Rahmani}: textit{Spatial modelization: local linear estimation of the conditional distribution for functional data.} Spatial Statistics. textbf{6} ,(2013), pp. 1-23.

bibitem{16} {sc N. Ling, {rm and} Q. Xu}:textit{ Asymptotic normality of conditional density estimation in the single index model for functional time series data}. Statistics and Probability Letters . textbf{82}, (2012), 2235-2243.

bibitem{2022m} {sc M. Mohammedi, S. Bouzebda, A. Laksaci {rm and} O. Bouanani} textit{ Asymptotic normality of the k-NN single index regression estimator for functional weak dependence data}, Communications in Statistics - Theory and Methods,(2022), DOI: 10.1080/03610926.2022.2150823

bibitem{MD11} {sc S. Muller, {rm and} J. Dippon}textit{ k-NN kernel estimate for nonparametric functional regression in time series analysis. } Fachbereich Mathematik, Fakultat Mathematik Und Physik (Pfaffenwaldring 57) . textbf{14},(2011), pp. 2011.

bibitem{2} {sc J. Ramsay, {rm and} B. Silverman} . textit{Functional Data Analysis Springer-Verlag.} New York . (1997)

bibitem{100} {sc D. Ruppert, {rm and} M. Wand} textit{Multivariate locally weighted least squares regression.} The Annals Of Statistics. (1994), pp. 1346-1370

bibitem{17} {sc P. Sang, {rm and} J. Cao}: textit{Functional single-index quantile regression models}. Statistics And Computing, (2020), pp. 1-11



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