Modeling Conditional Distributions for Functional Responses, With Application to Traffic Monitoring via GPS-Enabled Mobile Phones

REFERENCES

• Benko, M., Härdle, W., and Kneip, A. (2009), “Common Functional Principal Components,” The Annals of Statistics, 37, 1–34.
   Web of Science ®Google Scholar
• Bickel, P., and Li, B. (2007), “Local Polynomial Regression on Unknown Manifolds,” Complex Datasets and Inverse Problems: Tomography, Networks and Beyond, IMS Lecture Notes-Monograph Series, 54, 177–186.
   Google Scholar
• Cardot, H. (2007), “Conditional Functional Principal Components Analysis,” Scandinavian Journal of Statistics, 34, 317–335.
   Web of Science ®Google Scholar
• Cardot, H., Crambes, C., and Sarda, P. (2005), “Quantile Regression When the Covariates are Functions,” Journal of Nonparametric Statistics, 17, 841–856.
   Web of Science ®Google Scholar
• Chen, K., and Müller, H.-G. (2011), “Conditional Quantile Analysis When Covariates are Functions, With Application to Growth Data,” Journal of the Royal Statistical Society, 73.
   Google Scholar
• Chiou, J.-M., and Müller, H.-G. (2009), “Modeling Hazard Rates as Functional Data for the Analysis of Cohort Lifetables and Mortality Forecasting,” Journal of the American Statistical Association, 104, 572–585.
   Web of Science ®Google Scholar
• Chiou, J.-M., Müller, H.-G., and Wang, J.-L. (2004), “Functional Response Models,” Statistica Sinica, 14, 675–693.
   Web of Science ®Google Scholar
• Chu, L., Oh, S., and Recker, W. (2005), “Adaptive Kalman Filter Based Freeway Travel Time Estimation,” 84th TRB Annual Meeting, Washington, DC.
   Google Scholar
• Fan, J., and Gijbels, I. (1996), Local Polynomial Modelling and its Applications, London: Chapman & Hall.
   Google Scholar
• Faraway, J.J. (1997), “Regression Analysis for a Functional Response,” Technometrics, 39, 254–261.
   Web of Science ®Google Scholar
• Flury, B. (1988), Common Principal Components and Related Multivariate Models, New York: Wiley.
   Google Scholar
• Hall, P., and Hosseini-Nasab, M. (2006), “On Properties of Functional Principal Components Analysis,” Journal of the Royal Statistical Society, Series B, 68, 109–126.
   Google Scholar
• Hall, P., Müller, H.-G., and Yao, F. (2008), “Modeling Sparse Generalized Longitudinal Observations With Latent Gaussian Processes,” Journal of the Royal Statistical Society, Series B, 70, 730–723.
   Google Scholar
• Hall, P., Müller, H.-G., and Yao, F. (2009), “Estimation of Functional Derivatives,” The Annals of Statistics, 37, 3307–3329.
   Web of Science ®Google Scholar
• Herrera, J., and Bayen, A. (2010a), “Incorporation of Lagrangian Measurements in Freeway Traffic State Estimation,” Transportation Research Part B: Methodological, 44, 460–481.
   Web of Science ®Google Scholar
• Herrera, J., and Bayen, A. (2010b), “Incorporation of Lagrangian Measurements in Freeway Traffic State Estimation,” Transportation Research Part B: Methodological, 44, 460–481.
   Web of Science ®Google Scholar
• Herrera, J., Work, D., Herring, R., Ban, X., Jacobson, Q., and Bayen, A. (2010), “Evaluation of Traffic Data Obtained via GPS-Enabled Mobile Phones: The Mobile Century Field Experiment,” Transportation Research C, 18, 568–583.
   Web of Science ®Google Scholar
• Herring, R., Hofleitner, A., Amin, S., Nasr, T., Khalek, A., Abbeel, P., and Bayen, A. (2010), “Using Mobile Phones to Forecast Arterial Traffic Through Statistical Learning,” 89th Transportation Research Board Annual Meeting, Washington, DC.
   Google Scholar
• Izadpanah, P., Hellinga, B., and Fu, L. (2011), “Real-Time Freeway Travel Time Prediction Using Vehicle Trajectory Data,” Transportation Research Board 90th Annual Meeting, no. 11-2826.
   Google Scholar
• Jiang, C., and Wang, J. (2010), “Covariate Adjusted Functional Principal Component Analysis,” The Annals of Statistics, 38, 1194–1226.
   Web of Science ®Google Scholar
• Mammen, E., and Park, B.U. (2005), “Bandwidth Selection for Smooth Backfitting in Additive Models,” The Annals of Statistics, 33, 1260–1294.
   Web of Science ®Google Scholar
• Mazare, P.-E., Tossavainen, O.-P., Bayen, A., and Work, D. (2012), “Trade-Offs Between Inductive Loops and GPS Probe Vehicles for Travel Time Estimation: A Mobile Century Case Study,” Transportation Research Board 91st Annual Meeting (TRB’12).
   Google Scholar
• Mihaylova, L., Boel, R., and Hegyi, A. (2007), “Freeway Traffic Estimation Within Recursive Bayesian Framework,” Automatica, 43, 290–300.
   Web of Science ®Google Scholar
• Müller, H.-G., Chiou, J.-M., and Leng, X. (2008), “Inferring Gene Expression Dynamics via Functional Regression Analysis,” BMC Bioinformatics, 9, 60.
   PubMed Web of Science ®Google Scholar
• Müller, H.-G., and Yao, F. (2006), “Regressing Longitudinal Response Trajectories on a Covariate,” in Frontiers in Statistics. Festschrift for Peter Bickel, eds. J. Fan and H. L. Koul,, London: Imperial College Press, pp. 305–324.
   Google Scholar
• Müller, H.-G., and Yao, F. (2008), “Functional Additive Models,” Journal of the American Statistical Association, 103, 1534–1544.
   Web of Science ®Google Scholar
• Müller, H.-G., and Yao, F. (2010), “Additive Modeling of Functional Gradients,” Biometrika, 97, 791–806.
   Web of Science ®Google Scholar
• Nanthawichit, C., Nakatsuji, T., and Suzuki, H. (2003), “Application of Probe-Vehicle Data for Real-Time Traffic-State Estimation and Short-Term Travel-Time Prediction on a Freeway,” Transportation Research Record: Journal of the Transportation Research Board, 1855, 49–59.
   Web of Science ®Google Scholar
• Ramsay, J.O., and Dalzell, C.J. (1991), “Some Tools for Functional Data Analysis,” Journal of the Royal Statistical Society, Series B, 53, 539–572.
   Google Scholar
• Ramsay, J.O., and Silverman, B.W. (2005), Functional Data Analysis (2nd ed.), Springer Series in Statistics, New York: Springer.
   Google Scholar
• Rice, J.A. (2004), “Functional and Longitudinal Data Analysis: Perspectives on Smoothing,” Statistica Sinica, 14, 631–647.
   Web of Science ®Google Scholar
• Shen, Q., and Faraway, J. (2004), “An F-test for Linear Models With Functional Responses,” Statistica Sinica, 14, 1239–1257.
   Web of Science ®Google Scholar
• Tao, S., Manolopoulos, V., Rodriguez, S., and Rusu, A. (2012), “Real-Time Urban Traffic State Estimation With A-GPS Mobile Phones as Probes,” Journal of Transportation Technologies, 2, 22–31.
   Google Scholar
• Wang, Y., and Nihan, N. (2000), “Freeway Traffic Speed Estimation With Single-Loop Outputs,” Transportation Research Record: Journal of the Transportation Research Board, 1727, 120–126.
   Web of Science ®Google Scholar
• Wang, Y., and Papageorgiou, M. (2005), “Real-Time Freeway Traffic State Estimation Based on Extended Kalman Filter: A General Approach,” Transportation Research Part B: Methodological, 39, 141–167.
   Web of Science ®Google Scholar
• Wang, Y., Papageorgiou, M., and Messmer, A. (2008), “Real-Time Freeway Traffic State Estimation Based on Extended Kalman Filter: Adaptive Capabilities and Real Data Testing,” Transportation Research Part A: Policy and Practice, 42, 1340–1358.
   Web of Science ®Google Scholar
• Work, D., Tossavainen, O., Blandin, S., Bayen, A., Iwuchukwu, T., and Tracton, K. (2008), “An Ensemble Kalman Filtering Approach to Highway Traffic Estimation Using GPS Enabled Mobile Devices,” Decision and Control, 2008. CDC 2008. 47th IEEE Conference, pp. 5062–5068.
   Google Scholar
• Yao, F., Müller, H.-G., and Wang, J.-L. (2005), “Functional Data Analysis for Sparse Longitudinal Data,” Journal of the American Statistical Association, 100, 577–590.
   Web of Science ®Google Scholar