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用于非参数曲线估计的一类新核函数AI 解读

We introduce a new class of variable kernels which depend on the smoothing parameter b through a simple scaling operation, and which have good integrated mean square error (IMSE) convergence properties. These kernels deform "automatically" near the boundary, eliminating boundary bias. Computational formulas are given for all orders of kernel in terms of exponentially damped sines and cosines. The kernel is a computationally convenient approximation to a certain Green's…

非参数泛函估计的最优代入估计量AI 解读

Consider the problem of estimating the value of a functional $\Lambda(f)$ for $f$ an unknown density or regression function. The straightforward plug-in estimator $\Lambda(\hat f)$ with $\hat f$ a particular estimate of $f$ achieves the optimal rate of convergence in the sense of Stone over bounded subsets of a Sobolev space for a broad class of linear and nonlinear functionals. For many functionals the rate calculation depends on a Frechet-like derivative of the functional,…