In this study, the statistical powers of Kolmogorov-Smimov two-sample （KS-2） and Wald Wolfowitz （WW） tests, non-parametric tests used in testing data from two independent samples, have been compared in terms of fi...In this study, the statistical powers of Kolmogorov-Smimov two-sample （KS-2） and Wald Wolfowitz （WW） tests, non-parametric tests used in testing data from two independent samples, have been compared in terms of fixed skewness and fixed kurtosis by means of Monte Carlo simulation. This comparison has been made when the ratio of variance is two as well as with equal and different sample sizes for large sample volumes. The sample used in the study is： （25, 25）, （25, 50）, （25, 75）, （25, 100）, （50, 25）, （50, 50）, （50, 75）, （50, 100）, （75, 25）, （75, 50）, （75, 75）, （75, 100）, （100, 25）, （100, 50）, （100, 75）, and （100, 100）. According to the results of the study, it has been observed that the statistical power of both tests decreases when the coefficient of kurtosis is held fixed and the coefficient of skewness is reduced while it increases when the coefficient of skewness is held fixed and the coefficient of kurtosis is reduced. When the ratio of skewness is reduced in the case of fixed kurtosis, the WW test is stronger in sample volumes （25, 25）, （25, 50）, （25, 75）, （25, 100）, （50, 75）, and （50, 100） while KS-2 test is stronger in other sample volumes. When the ratio of kurtosis is reduced in the case of fixed skewness, the statistical power of WW test is stronger in volume samples （25, 25）, （25, 75）, （25, 100）, and （75, 25） while KS-2 test is stronger in other sample volumes.展开更多
This article proposes a new lack-of-test based on the weighted ratio of residuals and variances for partially linear regression models. The large and small sampling properties of the proposed test are established. The...This article proposes a new lack-of-test based on the weighted ratio of residuals and variances for partially linear regression models. The large and small sampling properties of the proposed test are established. The testing procedure is illustrated via several examples. Simulation studies show that the testing procedures are powerful even in small samples. An application of the test to a real data set is presented.展开更多
文摘In this study, the statistical powers of Kolmogorov-Smimov two-sample （KS-2） and Wald Wolfowitz （WW） tests, non-parametric tests used in testing data from two independent samples, have been compared in terms of fixed skewness and fixed kurtosis by means of Monte Carlo simulation. This comparison has been made when the ratio of variance is two as well as with equal and different sample sizes for large sample volumes. The sample used in the study is： （25, 25）, （25, 50）, （25, 75）, （25, 100）, （50, 25）, （50, 50）, （50, 75）, （50, 100）, （75, 25）, （75, 50）, （75, 75）, （75, 100）, （100, 25）, （100, 50）, （100, 75）, and （100, 100）. According to the results of the study, it has been observed that the statistical power of both tests decreases when the coefficient of kurtosis is held fixed and the coefficient of skewness is reduced while it increases when the coefficient of skewness is held fixed and the coefficient of kurtosis is reduced. When the ratio of skewness is reduced in the case of fixed kurtosis, the WW test is stronger in sample volumes （25, 25）, （25, 50）, （25, 75）, （25, 100）, （50, 75）, and （50, 100） while KS-2 test is stronger in other sample volumes. When the ratio of kurtosis is reduced in the case of fixed skewness, the statistical power of WW test is stronger in volume samples （25, 25）, （25, 75）, （25, 100）, and （75, 25） while KS-2 test is stronger in other sample volumes.
基金partially supported by the Major Project of Humanities Social Science Foundation of Ministry of Education under Grant No.08JJD910247Key Project of Chinese Ministry of Education under Grant No. 108120+3 种基金National Natural Science Foundation of China under Grant No.11271368Beijing Natural Science Foundation under Grant No.1102021the Fundamental Research Funds for the Central Universitiesthe Research Funds of Renmin University of China under Grant Nos.10XNL018 and 11XNH107
文摘This article proposes a new lack-of-test based on the weighted ratio of residuals and variances for partially linear regression models. The large and small sampling properties of the proposed test are established. The testing procedure is illustrated via several examples. Simulation studies show that the testing procedures are powerful even in small samples. An application of the test to a real data set is presented.
