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Goodness-of-Fit Test for Monotone Functions

机译:单调函数的拟合优度检验

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In this article, we develop a test for the null hypothesis that a real-valued function belongs to a given parametric set against the non-parametric alternative that it is monotone, say decreasing. The method is described in a general model that covers the monotone density model, the monotone regression and the right-censoring model with monotone hazard rate. The criterion for testing is an L_p-distance between a Grenander-type non-parametric estimator and a parametric estimator computed under the null hypothesis. A normalized version of this distance is shown to have an asymptotic normal distribution under the null, whence a test can be developed. Moreover, a bootstrap procedure is shown to be consistent to calibrate the test.
机译:在本文中,我们针对零假设进行了检验,该假设是实值函数属于给定的参数集,而不是单调(即递减)的非参数替代。在涵盖单调密度模型,单调回归和具有单调危险率的右删失模型的通用模型中描述了该方法。测试的标准是Grenander型非参数估计量与在原假设下计算出的参数估计量之间的L_p距离。该距离的归一化版本显示为在零下具有渐近正态分布,从而可以进行检验。此外,引导程序显示出可以校准测试的一致性。

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