Recovering covariance from functional fragments
从函数数据片段恢复协方差
We consider nonparametric estimation of a covariance function on the unit square, given a sample of discretely observed fragments of functional data. When each sample path is observed only on a subinterval of length |$\delta<1$|, one has no statistical information on the unknown covariance outside a |$\delta$|-band around the diagonal. The problem seems unidentifiable without parametric assumptions, but we show that nonparametric estimation is feasible under suitable…