Smoothing: Computing Curves from Noisy Data

Abstract

The previous two chapters have introduced the Matlab and R code needed to specify basis function systems and then to define curves by combining these coefficient arrays. For example, we saw how to construct a basis object such as heightbasis to define growth curves and how to combine it with a matrix of coefficients such as heightcoef so as to define growth functional data objects such as were plotted in Figure 1.1.

We now turn to methods for computing these coefficients with more careful consideration of measurement error. For example, how do we compute these coefficients to obtain an optimal fit to data such as the height measurements for 54 girls in the Berkeley growth study stored in the 31 by 54 matrix that we name heightmat? Or how do we replace the rather noisy mean daily precipitation observations by smooth curves?