Nonparametric fixed-interval smoothing with vector splines

Nonparametric fixed-interval smoothing with vector splines

Nonparametric fixed-interval smoothing of nonlinear vector-valued measurements

This paper addresses the problem of estimating a smooth vector-valued function given noisy nonlinear vector-valued measurements of that function. We present a nonparametric optimality criterion for this estimation problem, and develop a computationally eficient iterative algorithm for its solution. The new criterion is the natural generalization of our earlier work on vector splines with linear...

Improved inference in nonparametric regression using Lk-Smoothing splines

Smoothing splines are one of the most popular approaches to nonparametric regression. Wahba (J. Roy. Statist. Soc. Set. B 40 (1978) 364-372; 45 (1983) 133-150) showed that smoothing splines are also Bayes estimates and used the corresponding prior model to derive interval estimates for the regression function. Although the interval estimates work well on a global basis, they can have poor local...

Smoothing with Cubic Splines

A spline function is a curve constructed from polynomial segments that are subject to conditions or continuity at their joints. In this paper, we shall present the algorithm of the cubic smoothing spline and we shall justify its use in estimating trends in time series. Considerable effort has been devoted over several decades to developing the mathematics of spline functions. Much of the intere...

Square-root information filtering and fixed-interval smoothing with singularities

The square-root information filter and smoother algorithms have been generalized to handle singular state transition matrices and perfect measurements. This has been done to allow the use of SRIF techniques for problems with delays and state constraints. The generalized algorithms use complete QR factorization to isolate deterministically known parts of the state and nonsingular parts of the st...