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Road trafficking description and short term travel time forecasting, with a classification method. (English) Zbl 1104.62127

Summary: The purpose of this work is, on the one hand, to study how to forecast road trafficking on highway networks and, on the other hand, to describe future traffic events. Here, road trafficking is measured by vehicle velocities. The authors propose two methodologies. The first is based on an empirical classification method, and the second on a probability mixture model. They use an SAEM-type algorithm (a stochastic approximation of the EM algorithm) to select the densities of the mixture model. Then, they test the validity of their methodologies by forecasting short term travel times.

MSC:

62P99 Applications of statistics
62H30 Classification and discrimination; cluster analysis (statistical aspects)
90B20 Traffic problems in operations research
62P30 Applications of statistics in engineering and industry; control charts
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[1] Baraud, Model selection for regression on a fixed design, Probability Theory and Related Fields 117 pp 467– (2000) · Zbl 0997.62027
[2] Barron, Risk bounds for model selection via penalization, Probability Theory and Related Fields 113 pp 301– (1999)
[3] Basford, Estimation of allocation rates in a cluster analysis context, Journal of the American Statistical Association 80 pp 286– (1985)
[4] Belomestny, Completion and continuation of nonlinear traffic time series: a probabilistic approach, Journal of Physics A: Mathematical and General 36 pp 11369– (2003) · Zbl 1048.90060
[5] Besse, Approximation spline de la prévision d’un processus fonctionnel autorégressif d’ordre 1, The Canadian Journal of Statistics 14 pp 467– (1996)
[6] Birgé, Minimum contrast estimators on sieves: exponential bounds and rates of convergence, Bernoulli 4 pp 329– (1998) · Zbl 0954.62033
[7] Birgé, Gaussian model selection, Journal of the European Mathematical Society 3 pp 203– (2001) · Zbl 1037.62001
[8] Bosq, Processus linéaires vectoriels et prédiction, Comptes rendus mathématiques, Académie des sciences de Paris 337 pp 115– (2003) · Zbl 1025.60020 · doi:10.1016/S1631-073X(03)00274-7
[9] Breiman, Classification and Regression Trees (1984)
[10] Broniatowski, Reconnaissance de mélanges de densités par un algorithme d’apprentissage probabiliste pp 359– (1983)
[11] Celeux, Classification et modèles, Revue de statistique appliquée 36 pp 43– (1988) · Zbl 0972.62527
[12] G. Celeux, D. Chauveau & G. Diebol (1995). On Stochastic Versions of the EM Algorithm. Unpublished research report (Rapport de recherche), INRIA, no 2514.
[13] Celeux, A stochastic approximation type EM algorithm for the mixture problems, Stochastics Reports 41 pp 119– (1992) · Zbl 0766.62050
[14] Chen, Optimal rate of convergence for finite mixture models, The Annals of Statistics 23 pp 221– (1995)
[15] Cheng, The consistency of estimators in finite mixture models, Scandinavian Journal of Statistics 28 pp 603– (2001) · Zbl 1010.62023
[16] S. Cohen (1990). Ingénierie du trafic routier. Presses de l’École nationale des ponts et chaussées & L’Institut National de Recherche sur les Transports et leur Sécurité (INRETS), Arcueil, France.
[17] Couton, Application des mélanges de lois de probabilité à la reconnaissance de régimes de trafic routier, Recherche Transports Sécurité 53 pp 49– (1996)
[18] M. Danech-Pajouh & M. Aron (1994). ATHENA: Prévision à court terme du trafic sur une section de route. L’Institut National de Recherche sur les Transports et leur Sécurité (INRETS), Arcueil, France.
[19] Dazy, L’analyse de données évolutives (1996)
[20] Delyon, Convergence of a stochastic approximation version of the EM algorithm, The Annals of Statistics 27 pp 94– (1999) · Zbl 0932.62094
[21] Dempster, Maximum likelihood from incomplete data via the EM algorithm, Journal of the Royal Statistical Society, Series B 39 pp 1– (1977) · Zbl 0364.62022
[22] T. Dochy (1995). Arbres de régression et réseaux de neurones appliqués à la prévision de trafic routier. Thèse de l’Université Paris-Dauphine, Paris, France.
[23] Ferraty, Curves discrimination: a nonparametric functional approach, Computational Statistics and Data Analysis 44 pp 161– (2003) · Zbl 1429.62241
[24] Ferraty, Nonparametric models for functional data, with application in regression, time-series prediction and curve discrimination, Journal of Nonparametric Statistics 16 pp 111– (2004) · Zbl 1049.62039
[25] F. Gamboa, J.-M. Loubes & É. Maza (2005). Structural estimation for high dimensional data. Unpublished research report.
[26] Gordon, Classification (1999)
[27] Jambu, Classification automatique pour l’analyse des données. I (1978) · Zbl 0419.62057
[28] Kneip, Nonparametric estimation of common regressors for similar curve data, The Annals of Statistics 22 pp 1386– (1994) · Zbl 0817.62029
[29] Kneip, Statistical tools to analyze data representing a sample of curves, The Annals of Statistics 20 pp 1266– (1992) · Zbl 0785.62042
[30] M. Lavielle (2002). On the use of Penalized Contrasts for Solving Inverse Problems. Unpublished research report.
[31] Lindsay, A review of semiparametric mixture models, Journal of Statistical Planning and Inference 47 pp 29– (1995) · Zbl 0832.62027
[32] McLachlan, On the bias and variance of some proportion estimators, Communications in Statistics: Simulation and Computation 11 pp 715– (1982) · Zbl 0508.62045
[33] McLeish, Likelihood methods for the discrimination problem, Biometrika 73 pp 397– (1986) · Zbl 0632.62057
[34] Núñez-Antón, Longitudinal data with nonstationary errors: a nonparametric three-stage approach, Test 8 pp 201– (1999)
[35] Preda, PLS approach for clusterwise linear regression on functional data pp 167– (2004)
[36] Ramsay, Some tools for functional data analysis, Journal of the Royal Statistical Society, Series B 53 pp 539– (1991) · Zbl 0800.62314
[37] Van Grol, DACCORD: On-line travel time prediction pp TBC– (1998)
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