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In this paper, we propose a functional analysis of a set of individualspace-speed profiles corresponding to speed as function of the distancetraveled by the vehicle from an initial point. This functional analysis beginswith a functional modeling of space-speed profiles and the study ofmathematical properties of these functions. Then, in a first step, a smoothingprocedure based on spline smoothing is developed in order to convert the rawdata into functional objets and to filter out the measurement noise asefficiently as possible. It is shown that this smoothing step leads to acomplex nonparametric regression problem that needs to take into account twoconstraints: the use of the derivative information, and a monotonicityconstraint. The performance of the proposed two-step estimator (smooth, andthen monotonize) is illustrated on simulation studies and a real data example.In a second step, we use a curve registration method based on landmarksalignment in order to construct an average speed profile representative of aset of individual speed profiles. Finally, the variability of such a set isexplored by the use of functional boxplots.

A functional analysis of speed profiles: smoothing using derivative information, curve registration, and functional boxplot