Data-Driven Rank Tests for Independence

Journal of the American Statistical Association

Volumn 94, Issue 445, 1999, Pages 285-301

  Kallenberg, Wilbert C M ^a   Ledwina, Teresa ^b  

^a UNIVERSITY OF TWENTE   (Netherlands)

^b INSTITUTE OF MATHEMATICS   (Poland)

Author keywords

Consistency; Copula; Correlation; Independence; Model selection; Monte Carlo study; Rank test

Indexed keywords

EID: 0442325003     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.1999.10473844     Document Type: Article

References (37)

1. Behnen, K., and Neuhaus, G. (1989), Rank Tests With Estimated Scores and Their Application, Stuttgart: Teubner.
2. Blum, J. R., Kiefer, J., and Rosenblatt, M. (1961), “Distribution-Free Tests of Independence Based on the Sample Distribution Function,” The Annals of Mathematical Statistics, 32, 485-498.
3. Bogdan, M. (1995), “Data-Driven Smooth Tests for Bivariate Normality,” Technical Report 48, Institute of Mathematics, Technical University of Wroclaw.
4. Breiman, L. (1968), Probability, Reading, MA: Addison-Wesley.
5. Bryson, M. C., and Johnson, M. E. (1982), “Constructing and Simulating Multivariate Distributions Using Khinchine’s Theorem,” Journal of Statistical Computation and Simulation, 16, 129-137.
6. Chambers, J. M., Mallows, C. L., and Stuck, B. W. (1976), “A Method for Simulating Stable Random Variables,” Journal of the American Statistical Association, 71, 340-344.
7. Devroye, L. (1986), Non-Uniform Random Variate Generation, New York: Springer-Verlag.
8. Eubank, R. L., Hart, J. D., Simpson, D. G., and Stefanski, L. A. (1995), ‘Testing for Additivity in Nonparametric Regression,” The Annals of Statistics, 23, 1896-1920.
9. Eubank, R. L., LaRiccia, V. N., and Rosenstein, R. (1987), “Test Statistics Derived as Components of Pearson’s Phi-Squared Distance Measure,” Journal of the American Statistical Association, 82, 816-825.
10. Ferguson, T. S. (1995), “A Class of Symmetric Bivariate Uniform Distributions,” Statistical Papers, 36, 31-40.
11. Genest, C. (1987), “Frank’s Family of Bivariate Distributions,” Biometrika, 14, 549-555.
12. Inglot, T. Kallenberg, W. C. M., and Ledwina, T. (1997), “Data-Driven Smooth Tests for Composite Hypotheses,” The Annals of Statistics, 25, 1222-1250.
13. Inglot, T. and Ledwina, T. (1996), “Asymptotic Optimality of Data-Driven Neyman’s Tests,” The Annals of Statistics, 24, 1982-2019.
14. Johnson, M. E. (1987), Multivariate Statistical Simulation, New York: Wiley.
15. Johnson, N. L., and Kotz, S. (1972), Distributions in Statistics: Continuous Multivariate Distributions, New York: Wiley.
16. Kallenberg, W. C. M., and Ledwina, T. (1995a), “On Data-Driven Neyman’s Tests,” Probability and Mathematical Statistics, 15, 409-426.
17. Kallenberg, W. C. M., and Ledwina, T. (1995b), “Consistency and Monte Carlo Simulation of a Data-Driven Version of Smooth Goodness-of-Fit Tests,” The Annals of Statistics, 23, 1594-1608.
18. Kallenberg, W. C. M., and Ledwina, T. (1997a), “Data-Driven Smooth Tests for Composite Hypotheses: Comparison of Powers,” Journal of Statistical Computation and Simulation, 59, 101-121.
19. Kallenberg, W. C. M., and Ledwina, T. (1997b), “Data-Driven Smooth Tests When the Hypothesis Is Composite,” Journal of the American Statistical Association, 92, 1094-1104.
20. Kallenberg, W. C. M., Ledwina, T. and Rafajlowicz, E. (1997), “Testing Bivariate Independence and Normality,” Sankhya, Ser. A, 59, 42-59.
21. Kendall, M. G., and Buckland, W. R. (1957), A Dictionary of Statistical Terms, Edinburgh: Oliver and Boyd.
22. Koziol, J. A. (1979), “A Smooth Test for Bivariate Independence,” Sankhya, Ser. B, 41, 260-269.
23. Lancaster, H. O. (1969), The Chi-Squared Distribution, New York: Wiley.
24. Lawrance, A. J., and Lewis, P. A. W. (1983), “Simple Dependent Pairs of Exponential and Uniform Random Variables,” Operations Research, 31, 1179-1197.
25. Ledwina, T. (1986), “Large Deviations and Bahadur Slopes of Some Rank Tests of Independence,” Sankhyà, Ser. A, 48, 188-207.
26. Ledwina, T. (1994), “Data-Driven Version of Neyman’s Smooth Test of Fit,” Journal of the American Statistical Association, 89, 1000-1005.
27. Lehmann, E. L. (1975), Nonparametrics. Statistical Methods Based on Ranks, Oakland, CA: Holden-Day.
28. Marshall, A. W., and Olkin, I. (1967), “A Multivariate Exponential Distribution,” Journal of the American Statistical Association, 62, 30-44.
29. Massart, P. (1990), ‘The Tight Constant in the Dvoretzky-Kiefer- Wolfowitz Inequality,” The Annals of Probability, 18, 1269-1283.
30. Patil, S. A. (1969), “A Bivariate Distribution of Product of Beta Variables and Square Root of Chi-Squared Variable,” Sankhyà, Ser. B, 31, 25-28.
31. Prohorov, A. V. (1973), “On Sums of Random Vectors,” Theory of Probability and Its Applications, 18, 186-188.
32. Raftery, A. E. (1984), “A Continuous Multivariate Exponential Distribution,” Communications in Statistics, Part A-Theory and Methods, 13, 947-965.
33. Samorodnitsky, G., and Taqqu, M. S. (1994), Stable Non-Gaussian Random Processes: Stochastic Models With Infinite Variance, New York: Chapman and Hall.
34. Sansone, G. (1959), Orthogonal Functions. New York: Interscience.
35. Schwarz, G. (1978), “Estimating the Dimension of a Model,” The Annals of Statistics, 6, 461-464.
36. Schweizer, B., and Wolff, E. F. (1981), “On Nonparametric Measures of Dependence for Random Variables,” The Annals of Statistics, 9, 879-885.
37. Simonoff, J. S. (1990), Smoothing Methods in Statistics, New York: Springer-Verlag.