Testing Goodness-of-Fit Based on a Roughness Measure

A test for the one-sample goodness-of-t problem is proposed. The test is based on a distance that measures the diierence, 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.