Optimal Tests for the General Two-Sample Problem

Journal of Multivariate Analysis

Volumn 74, Issue 1, 2000, Pages 1-35

  Ferger, Dietmar ^a  

^a DRESDEN UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Two sample test, contiguous alternatives, local power, optimality, Brownian bridge with trend, functional data

Indexed keywords

EID: 0346487301     PISSN: 0047259X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmva.1999.1879     Document Type: Article

References (35)

1. 2-norm of multivariate probability density functions. Nonparametric Statist. 2:1993;169-181.
2. Bahr R. A New Test for the Multi-Dimensional Two-Sample Problem with General Alternatives. 1996;University of Hannover.
3. Beibel M. Sequential change-point detection in continuous time when the post-change drift is unknown. Bernoulli. 3:1997;457-478.
4. Bhattacharya P. K., Brockwell P. J. The minimum of an additive process with applications to signal estimation and storage theory. Z. Wahrsch. Verw. Gebiete. 37:1976;51-75.
5. Billingsley P. Convergence of Probability Measures. 1968;Wiley, New York.
6. Carlstein E. Nonparametric change-point estimation. Ann. Statist. 16:1988;188-197.
7. Csörgo M., Horváth L. Weighted Approximations in Probability and Statistics. 1993;Wiley, New York.
8. Darkhovski B. S. A nonparametric method for the a posteriori detection of the "disorder" time of a sequence of independent random variables. Theory Probab. Appl. 21:1976;178-183.
9. Darkhovski B. S. Nonparametric methods in change-point problems: A general approach and some concrete algorithms. IMS Lecture Notes Monographs Series. 1994;. p. 99-107.
10. Dümbgen L. The asymptotic behavior of some nonparametric change-point estimators. Ann. Statist. 19:1991;1471-1495.
11. m and measure-valued martingales. technical report. 1998.
12. Epps T. W., Singleton K. J. An omnibus test for the two-sample problem using the empirical characteristic function. J. Statist. Comput. Simul. 26:1986;177-203.
13. Ferger D. An extension of the Csörgo-Horváth functional limit theorem and its applications to change-point problems. J. Multivariate Anal. 51:1994a;338-351.
14. Ferger D. On the power of nonparametric change-point tests. Metrika. 41:1994b;277-297.
15. Ferger D. Change-Point Estimators Based on Weighted Empirical Processes with Applications to the Two-Sample Problem in General Measurable Spaces. 1995;University of Giessen.
16. D. Ferger, Optimal change-point detection, unpublished manuscript, Dresden University of Technology, 1997.
17. Ferger D. Testing for the existence of a Change-Point in a specified time interval. Advances in Stochastic Models for Reliability, Quality and Safety. 1998;Birkhäuser, Boston/Basel/Berlin. p. 277-289.
18. E. Gombay, and, L. Horáth, Approximations for the time of change and the powerfunction in change-point models, preprint, 1993.
19. Grenander U. Stochastic processes and statistical inferences. Ark. Mat. 1952;195-277.
20. Hájek J., Šidák Z. Theory of Rank Tests. 1967;Academic Press, New York.
21. Henze N. A multivariate two-sample test based on the number of nearest neighbor type coincidences. Ann. Statist. 16:1988;772-783.
22. Henze N., Voigt B. Almost sure convergence of certain slowly changing symmetric one- and multi-sample statistics. Ann. Probab. 20:1992;1086-1098.
23. Hettmansperger T. P., McKean J. W. Robust Nonparametric Statistical Methods. Kendall's Library of Statistics. 5:1998;Wiley, New York.
24. Hinkley C. V. Inference about the change-point in a sequence of random variables. Biometrika. 57:1970;1-17.
25. Hollander M., Wolfe D. A. Nonparametric Statistical Methods. 1973;Wiley, New York.
26. M. Hušková, Tests and estimators for the change-point problem based on M-statistics, preprint, Charles University of Praha, 1996.
27. Karatzas I., Shreve S. E. Brownian Motion and Stochastic Calculus. Graduate Texts in Mathematics. 113:1988;Springer-Verlag, New York/Berlin/Heidelberg/London/Paris/Tokyo.
28. Lehmann E. L. Nonparametrics: Statistical Methods Based on Ranks. 1975;Holden-Day, San Francisco.
29. Liptser R. S., Shiryayev A. N. Statistics of Random Processes I. 1977;Springer-Verlag, Berlin.
30. Lombard F., Hart J. D. The analysis of change-point data with dependent errors. IMS Lecture Notes Monograph Series. 1994;. p. 194-209.
31. Ramsay J. O., Silverman B. W. Functional Data Analysis. 1997;Springer-Verlag, New York.
32. Shorack G. R., Wellner J. A. Empirical Processes with Applications to Statistics. 1986;Wiley, New York.
33. Szyszkowicz B. Change-point problems and contiguous alternatives. Statist. Probab. Lett. 11:1991;299-308.
34. Todorivic P. An Introduction to Stochastic Processes and Their Applications. 1992;Springer-Verlag, New York.
35. Yao Y.-C., Huang D., Davis R. On almost sure behavior of change-point estimators. IMS Lecture Notes Monograph Series. 1994;. p. 359-371.