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Yuedong Wang 《统计学通讯:模拟与计算》2013,42(2):765-782
Wahba, Wang, Gu, Klein and Klein introduced Smoothing Spline ANalysis of VAriance (SS ANOVA) method for data from exponential families. Based on RKPACK, which fits SS ANOVA models to Gaussian data, we introduce GRKPACK a collection of Fortran subroutines for binary, binomial, Poisson and Gamma data. We also show how to calculate Bayesian confidence intervals for SS ANOVA estimates. 相似文献
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The smoothing spline method is used to fit a curve to a noisy data set, where selection of the smoothing parameter is essential. An adaptive Cp criterion (Chen and Huang 2011) based on the Stein’s unbiased risk estimate has been proposed to select the smoothing parameter, which not only considers the usual effective degrees of freedom but also takes into account the selection variability. The resulting fitted curve has been shown to be superior and more stable than commonly used selection criteria and possesses the same asymptotic optimality as Cp. In this paper, we further discuss some characteristics on the selection of smoothing parameter, especially for the selection variability. 相似文献
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In a smoothing spline model with unknown change-points, the choice of the smoothing parameter strongly influences the estimation of the change-point locations and the function at the change-points. In a tumor biology example, where change-points in blood flow in response to treatment were of interest, choosing the smoothing parameter based on minimizing generalized cross-validation (GCV) gave unsatisfactory estimates of the change-points. We propose a new method, aGCV, that re-weights the residual sum of squares and generalized degrees of freedom terms from GCV. The weight is chosen to maximize the decrease in the generalized degrees of freedom as a function of the weight value, while simultaneously minimizing aGCV as a function of the smoothing parameter and the change-points. Compared with GCV, simulation studies suggest that the aGCV method yields improved estimates of the change-point and the value of the function at the change-point. 相似文献
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Let Xi≤?≤Xm and Yi≤?≤Yn be two sets of independent order statistics from continous distributions with distribution functions F and G respectively. Let Ri denote the rank of Xi in the combined order sample. Steck (1980) has found an expression for P(bi≤Ri≤ai, all i) when F = h(G), h being the incomplete beta function with parameters (α,β?α+1). An alternative expression for the same probability is obtained which is computationally a substantial improvement on Steck's result. 相似文献