![]() ![]() ![]() We further consider a nontrivial extension of the local smoothness of inhomogeneous two-dimensional functions or spatial fields. A successful estimate of the local smoothness is useful for identifying abrupt changes of smoothness of the data, performing functional clustering and improving the uniformity of coverage of the confidence intervals of smoothing splines. The proposed method provides full information of the local smoothness at every location on the entire data domain, so that it is able to understand the degrees of spatial inhomogeneity of the function. In this paper, we propose a new nonparametric method to estimate local smoothness of the function based on a moving local risk minimization coupled with spatially adaptive smoothing splines. Most existing studies related to this problem deal with estimation induced by a single smoothing parameter or partially local smoothing parameters, which may not be efficient to characterize various degrees of smoothness of the underlying function. We consider a problem of estimating local smoothness of a spatially inhomogeneous function from noisy data under the framework of smoothing splines. ![]()
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