A Simulation Study of Power Comparison of Goodness-of-Fit Tests رسالة ماجستير

Abstract

The main purpose of this thesis is to study and compare the power of five goodness-of-fit(GOF) tests: Chi-square(𝜒2) test, Kolmogorov-Smirnov(KS) test, Cramér-von Mises (CVM) test, Anderson-Darling(AD) test and Bickel-Rosenblatt(BR) test under several parametric and non-parametric alternatives. Power comparisons of these five tests were obtained by using Monte Carlo simulation method of sample data generated from parametric and non-parametric alternatives and the parametric alternatives follow symmetric and non-symmetric distributions, R software was used to generate data for simulations purpose. Two significance levels 5% and 10% were used and the critical values for power comparisons were obtained based on 10000 simulated samples from different null distributions. 10000 samples each of size n = 10, 20, 30, 40, 50, 100, 200, 300, 400, 500, 1000, and 2000 were generated from each of the given alternatives. The power of each test was then obtained by comparing the GOF test statistics with the respective critical values. Simulation results show that the AD test has a higher power in the case of testing symmetric distributions and the data were generated from parametric alternative distributions followed by the CVM and the KS tests while the 𝜒2 test has the lowest power. The BR test has a higher power in the case of testing symmetric distributions and the data were generated from some non-parametric alternative distributions and the AD test has a higher power under other non-parametric alternative distributions. This study also shows that the BR test has a higher power when using the Epanechnikov kernel compared to the uniform kernel.