NONPARAMETRIC FIXED-INTERVAL SMOOTHING WITH VECTOR SPLINES

Spline smoothing has become a popular method for nonparametric exploration and estimation of scalar-valued functions, but its generalizations to vector-valued functions have been underutilized. This paper presents a computationally efficient algorithm for nonparametric smoothing of vector signals with general measurement covariances. This new algorithm provides an alternative to the prevalent "optimal" smoothing algorithms that hinge on (possibly inaccurate) parametric state-space models. We develop and compare automatic procedures that use the measurements to determine how much to smooth; this adaptation allows the data to "speak for itself" without imposing a Gauss-Markov model structure. We present a nonparametric approach to covariance estimation for the case of i.i.d. measurement errors. Monte Carlo simulations demonstrate the performance of the algorithm.