Robust functional principal components for sparse longitudinal data

In this paper we review existing methods for robust functional principal component analysis (FPCA) and propose a new method FPCA that can be applied to longitudinal data where only few observations per trajectory are available. This is against the presence of atypical observations, also used derive non-robust approach sparsely observed data. We use local regression estimate values covariance function, taking advantage fact elliptically distributed random vectors conditional location parameter some its components given others linear function conditioning set. observation allows us obtain estimators by using methods. The finite sample performance our proposal explored through simulation study shows that, as expected, outperforms alternatives when contaminated. Furthermore, see samples do not contain outliers variant compares favourably alternative in literature. A real example presented.