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函数值随机过程建模及其生育动态应用AI 解读

Summary We introduce a simple and interpretable model for functional data analysis for situations where the observations at each location are functional rather than scalar. This new approach is based on a tensor product representation of the function-valued process and utilizes eigenfunctions of marginal kernels. The resulting marginal principal components and product principal components are shown to have nice properties. Given a sample of independent realizations of the…

基于平滑截断的局部似然密度估计AI 解读

Two existing density estimators based on local likelihood have properties that are comparable to those of local likelihood regression but they are much less used than their counterparts in regression. We consider truncation as a natural way of localising parametric density estimation. Based on this idea, a third local likelihood density estimator is introduced. Our main result establishes that the three estimators coincide when a free multiplicative constant is used as an…