Power Comparison of Independence Test for the Farlie-Gumbel-Morgenstern Family

Title & Authors
Power Comparison of Independence Test for the Farlie-Gumbel-Morgenstern Family

Abstract
Developing a test for independence of random variables X and Y against the alternative has an important role in statistical inference. Kochar and Gupta (1987) proposed a class of tests in view of Block and Basu (1974) model and compared the powers for sample sizes n = 8, 12. In this paper, we evaluate Kochar and Gupta (1987) class of tests for testing independence against quadrant dependence in absolutely continuous bivariate Farlie-Gambel-Morgenstern distribution, via a simulation study for sample sizes n = 6, 8, 10, 12, 16 and 20. Furthermore, we compare the power of the tests with that proposed by G$\small{\ddot{u}}$uven and Kotz (2008) based on the asymptotic distribution of the test statistics.
Keywords
Negative and positive quadrant dependence;Farlie-Gambel-Morgenstern distribution;U-Statistics;
Language
English
Cited by
1.
Aspects of Dependence in Generalized Farlie-Gumbel-Morgenstern Distributions, Communications in Statistics - Simulation and Computation, 2011, 40, 8, 1192
References
1.
Bairamov, I. and Kotz, S. (2002). Dependence structure and symmetry of Huang-Kotz FGM distributions and their extensions, Metrika, 56, 55-72.

2.
Block, H. W. and Basu, A. P. (1974). A continuous bivariate exponential extension, Journal of the American Statistical Association, 69, 1031-1037.

3.
Farlie, D. J. G. (1960). The performance of some correlation coefficients for a general bivariate distribution function, Biometrika, 47, 307-323.

4.
Gibbons, J. D. (1971). Nonparametric Statistical Inference, MaGraw-Hill.

5.
Gumbel, E. J. (1958). Statistics of Extremes, Columbia University Press, New York.

6.
Guven, B. and Kotz, S. (2008). Test of independence for generalized Farlie-Gumbel-Morgenstern distributions, Journal of Computational and Applied Mathemathics, 212, 102-111.

7.
Hanagal, D. D. and Kale, B. K. (1991). Large sample tests of independence for absolutely continuous bivariate exponential distribution, Communications in Statistics - Theory and Methods, 20, 1301-1313.

8.
Kochar, S. G. and Gupta, R. P. (1987). Competitors of Kendall-tau test for testing independence against PQD, Biometrika, 74, 664-669.

9.
Kochar, S. G. and Gupta, R. P. (1990). Distribution-free tests based on sub-sample extrema for testing against positive dependence, Australian Journal of Statistics, 32, 45-51.

10.
Koroljuk, V. S. and Borovskich, Y. V. (1994). Theory of U-statistic, Kluwer Academic Publishers.

11.
Lehmann, E. L. (1966). Some concepts of dependence, The Annals of Mathematical Statistics, 37, 1137-1153.

12.
Mari, D. D. and Kotz, S. (2001). Correlation and Dependence, Imperical College Press.

13.
Modarres, R. (2007). A test of independence based on the likelihood of Cut-Points, Communicationa in Statistics-Simulation and Computation, 36, 817-825.

14.
Morgenstern, D. (1956). Einfache Beispiele Zweidimensionaler Verteilungen, Mitteilungsblatt fur Mathematische Statistik, 8, 234-235.

15.
Serfling, R. J. (1980). Approximations Theorems of Mathematical Statistics, John Wiley & Sons.

16.
Shetty, I. D. and Pandit, P. V. (2003). Distribution-free tests for independence against positive quadrant dependence: A generalization, Statistical Methods and Application, 12, 5-17.