- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 538342, 11 pages
Degenerate-Generalized Likelihood Ratio Test for One-Sided Composite Hypotheses
School of Finance and Statistics, East China Normal University, Shanghai 200241, China
Received 19 January 2012; Revised 26 March 2012; Accepted 20 April 2012
Academic Editor: Ming Li
Copyright © 2012 Dongdong Xiang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- A. Wald, “Sequential tests of statistical hypotheses,” Annals of Mathematical Statistics, vol. 16, pp. 117–186, 1945.
- L. Weiss, “On sequential tests which minimize the maximum expected sample size.,” Journal of the American Statistical Association, vol. 57, pp. 551–566, 1962.
- T. L. Lai, “Optimal stopping and sequential tests which minimize the maximum expected sample size,” The Annals of Statistics, vol. 1, pp. 659–673, 1973.
- G. Lorden, “2-SPRT's and the modified Kiefer-Weiss problem of minimizing an expected sample size,” The Annals of Statistics, vol. 4, no. 2, pp. 281–291, 1976.
- M. D. Huffman, “An efficient approximate solution to the Kiefer-Weiss problem,” The Annals of Statistics, vol. 11, no. 1, pp. 306–316, 1983.
- L. Wang, D. Xiang, X. Pu, and Y. Li, “Double sequential weighted probability ratio test for one-sided composite hypotheses,” Communication in Statistics—Theory and Method. In press.
- T. L. Lai, “Nearly optimal sequential tests of composite hypotheses,” The Annals of Statistics, vol. 16, no. 2, pp. 856–886, 1988.
- B. Darkhovsky, “Optimal sequential tests for testing two composite and multiple simple hypotheses,” Sequential Analysis, vol. 30, no. 4, pp. 479–496, 2011.
- H. P. Chan and T. L. Lai, “Importance sampling for generalized likelihood ratio procedures in sequential analysis,” Sequential Analysis, vol. 24, no. 3, pp. 259–278, 2005.
- Y. Li and X. Pu, “Method of sequential mesh on Koopman-Darmois distributions,” Science China A, vol. 53, no. 4, pp. 917–926, 2010.
- Y. Li and X. Pu, “A method for designing three-hypothesis test problems and sequential schemes,” Communications in Statistics—Simulation and Computation, vol. 39, no. 9, pp. 1690–1708, 2010.
- M. Li, “A class of negatively fractal dimensional Gaussian random functions,” Mathematical Problems in Engineering, Article ID 291028, 18 pages, 2011.
- M. Li, C. Cattani, and S. Y. Chen, “Viewing sea level by a one-dimensional random function with long memory,” Mathematical Problems in Engineering, vol. 2011, Article ID 10.1155/2011/654284, 13 pages, 2011.
- M. Li and W. Zhao, “Variance bound of ACF estimation of one block of fGn with LRD,” Mathematical Problems in Engineering, vol. 2010, Article ID 560429, 14 pages, 2010.
- M. Li and W. Zhao, “Visiting power laws in cyber-physical networking systems,” Mathematical Problems in Engineering, vol. 2012, Article ID 302786, 13 pages, 2012.
- R. M. Phatarfod, “Sequential analysis of dependent observations. I,” Biometrika, vol. 52, pp. 157–165, 1965.
- A. Tartakovsky, “Asymptotically optimal sequential tests for nonhomogeneous processes,” Sequential Analysis, vol. 17, no. 1, pp. 33–61, 1998.
- A. Novikov, “Optimal sequential tests for two simple hypotheses,” Sequential Analysis, vol. 28, no. 2, pp. 188–217, 2009.
- R. Niu and P. K. Varshney, “Sampling schemes for sequential detection with dependent observations,” IEEE Transactions on Signal Processing, vol. 58, no. 3, part 2, pp. 1469–1481, 2010.
- T. L. Lai, “Information bounds and quick detection of parameter changes in stochastic systems,” IEEE Transactions on Information Theory, vol. 44, no. 7, pp. 2917–2929, 1998.
- H. Robbins and D. Siegmund, “A class of stopping rules for testing parametric hypotheses,” in Proceedings of the 6th Berkeley Symposium on Mathematical Statistics and Probability, vol. 4, pp. 37–41, University of California Press, Berkeley, Calif, USA, 1973.
- D. Han and F. Tsung, “A reference-free Cuscore chart for dynamic mean change detection and a unified framework for charting performance comparison,” Journal of the American Statistical Association, vol. 101, no. 473, pp. 368–386, 2006.
- Y.-M. Chou, R. L. Mason, and J. C. Young, “The SPRT control chart for standard deviation based on individual observations,” Quality Technology & Quantitative Management, vol. 3, no. 3, pp. 335–345, 2006.
- S. S. Shapiro and M. B. Wilk, “An analysis of variance test for normality: complete samples,” Biometrika, vol. 52, pp. 591–611, 1965.