SMOOTH TEST FOR TESTING EQUALITY OF TWO DENSITIES

It has been a conventional wisdom that the two-sample version of the goodness-of-fit test like the Kolmogorov-Smirnov, Cramér-von Mises and Anderson-Darling tests fail to have good power particularly against very specific alternatives. We show that a modified version of Neyman Smooth test that can also be derived as a score test based on the empirical distribution functions obtained from the two samples remarkably improves the detection of directions of departure. We can identify deviations in different moments like the mean, variance, skewness or kurtosis terms using the Ratio Density Function. We derive a bound on the relative sample sizes of the two samples for a consistent test and an "optimal" choice range of the sample sizes to ensure minimal size distortion in finite samples. We apply our procedure to compare the age distributions of employees insured with small employers