M-type smoothing spline ANOVA for correlated data

This paper concerns outlier robust non-parametric regression with smoothing splines for data that are possibly correlated. We define a robust smoother as the minimizer of a penalized robustified log likelihood. Our estimation algorithm uses iteratively reweighted least squares to estimate the regression function. We develop two types of robust methods for joint estimation of the smoothing parameters and the correlation parameters: indirect methods and direct methods, terms borrowed from the related generalized smoothing spline literature. The indirect methods choose those parameters by conveniently approximating the distribution of the working data at each iteration as Gaussian. The direct methods estimate those parameters to minimize an estimate of the loss between the truth and the final estimated regression. Indirect methods are computationally more efficient, but our empirical studies suggest that direct methods result in more accurate estimates. Finally, the methods are applied to a data set from a macaque Simian–Human Immunodeficiency Virus (SHIV) challenge study.