Smoothing Noisy Data with Spline Functions *
نویسنده
چکیده
I t is shown how to choose the smoothing parameter when a smoothing periodic spline of degree 2m -1 is used to reconstruct a smooth periodic curve from noisy ordinate data. The noise is assumed "white" , and the true curve is assumed to be in the Sobolev space W,(*ra) of periodic functions with absolutely continuous v-th derivative, v = 0, t . . . . . 2 m I and square integrable 2m-th derivative. The criteria is minimum expected square error, averaged over the data points. The dependency of the optimum smoothing parameter on the sample size, the noise variance, and the smoothness of the true curve is found explicitly.
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