Testing Goodness-of-Fit Based on a Roughness Measure
提出一种基于粗糙度量的单样本拟合优度检验，通过估计密度函数与假设密度函数在粗糙度上的差异来构建检验统计量，在高频备择和尖峰密度检测中具有较高功效，并与Kolmogorov-Smirnov检验进行了比较。
Abstract A test for the one-sample goodness-of-fit problem is proposed. The test is based on a distance that measures the difference, in terms of roughness, between the underlying density function and the hypothesized density function. One advantage of using a roughness measure is high power in detecting high-frequency alternatives and densities with sharp features. The test statistic that estimates the distance is derived from the viewpoint of kernel density estimation, and a testing procedure is developed based on the asymptotic distribution of the test statistic. The proposed test is compared to the Kolmogorov-Smirnov test.