Estimating Derivatives for Samples of Sparsely Observed Functions, With Application to Online Auction Dynamics
稀疏观测函数样本的导数估计及在线拍卖动态应用
It is often of interest to recover derivatives of a sample of random functions from sparse and noise-contaminated measurements, especially when the dynamics of underlying processes is of interest. We propose a novel approach based on estimating derivatives of eigenfunctions and expansions of random functions into their eigenfunctions to obtain a representation for derivatives. In combination with estimates for functional principal component scores for sparse data, this leads…