Robust functional estimation using the median and spherical principal components

We present robust estimators for the mean and the principal components of a stochastic process in L(2)(R). Robustness and asymptotic properties of the estimators are studied theoretically, by simulation and by example. It is shown that the proposed estimators are generally more robust to outliers than the commonly used sample mean and principal components, although their properties depend on the spacings of the eigenvalues of the covariance function.