Test for parameter change based on the estimator minimizing density-based divergence measures

Annals of the Institute of Statistical Mathematics

Volumn 57, Issue 3, 2005, Pages 553-573

  Lee, Sangyeol ^a   Okyoung, N A ^a  

^a Seoul National University   (South Korea)

Author keywords

Brownian bridge; Cusum test; Density based divergence measures; Robust property; Test for parameter changes; Weak convergence

Indexed keywords

BROWNIAN BRIDGE; CUSUM TEST; DENSITY-BASED DIVERGENCE MEASURES; ROBUST PROPERTY; TEST FOR PARAMETER CHANGES; WEAK CONVERGENCE;

COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; OPTIMIZATION; PROBLEM SOLVING; ROBUSTNESS (CONTROL SYSTEMS); STATISTICAL METHODS;

PARAMETER ESTIMATION;

EID: 29344461254     PISSN: 00203157     EISSN: 15729052     Source Type: Journal    
DOI: 10.1007/BF02509239     Document Type: Article

References (19)

1. Basu, A. and Lindsay, B. G. (1994). Minimum disparity estimation for continuous models: Efficiency, distributions and robustness, Annals of the Institute of Statistical Mathematics, 46, 683-705.
2. Basu, A., Harris, I. R., Hjort, N. L. and Jones, M. C. (1998). Robust and efficient estimation by minimizing a density power divergence, Biometrika, 85, 549-559.
3. Beran, R. (1977). Minimum hellinger distance estimates for parametric models, Annals of Statistics, 5, 445-463.
4. Bosq, D. (1996). Nonparametric Statistics for Stochastic Processes; Estimation and Prediction, Lecture Notes in Statistics, No. 10, Springer, New York.
5. Bustos, O. H. (1982). General M-estimates for contaminated pth-order autoregressive processes: Consistency and asymptotic normality, Zeitschrift fur Wahrscheinlichkeitstheorie und verwandte Gebiete, 59, 491-504.
6. Cao, R., Cuevas, A. and Fraiman, R. (1995). Minimum distance density-based estimation, Computational Statistics and Data Analysis, 20, 611-631.
7. Chan, J. and Gupta, A. K. (2000). Parametric Statistical Change Point Analysis, Birkhäuser, Boston.
8. Csörgo, M. and Horváth, L. (1997). Limit Theorems in Change-point Analysis, Wiley, New York.
9. Denby, L. and Martin, D. (1979). Robust estimation of the first-order autoregressive parameter, Journal of the American Statistical Association, 74, 140-146.
10. Ferguson, T. S. (1996). A Course in Large Sample Theory, Chapman & Hall, London.
11. Fox, A. J. (1972). Outliers in time series, Journal of the Royal Statistical Society. Series B, 34, 350-363.
12. Hong, C. and Kim, Y. (2001). Automatic selection of the tuning parameter in the minimum density power divergence estimation, Journal of the Korean Statistical Society, 30, 453-465.
13. Inclán, C. and Tiao, G. C. (1994). Use of cumulative sums of squares for retrospective detection of changes of variances, Journal of the American Statistical Association, 89, 913-923.
14. Lee, S. and Park, S. (2001). The cusum of squares test for scale changes in infinite order moving average processes, Scandinavian Journal of Statistics, 28, 625-644.
15. Lee, S., Ha, J., Na, O. and Na, S. (2003). The cusum test for parameter change in time series models, Scandinavian Journal of Statistics, 30, 781-796.
16. Page, E. S. (1955). A test for change in a parameter occurring at an unknown point, Biometrika, 42, 523-527.
17. Peligrad, M. (1986). Recent advances in the central limit theorem and its weak invariance principle for mixing sequences of random variables (a survey), Dependence in Probability and Statistics (eds. E. Eberlein and M. S. Taqqu), 193-223, Birkhäuser, Boston.
18. Simpson, D. G. (1987). Minimum hellinger distance estimation for the analysis of count data, Journal of the American Statistical Association, 82, 802-807.
19. Tamura, R. N. and Boos, D. D. (1986). Minimum hellinger distance estimation for multivariate location and covariance, Journal of the American Statistical Association, 81, 223-239.