Sequential change-point detection for skew normal distribution

REFERENCES

• Adcock, C., M. Eling, and N. Loperfido. 2015. “Skewed Distributions in Finance and Actuarial Science: A Review.” The European Journal of Finance 21 (13-14):1253–81. doi:10.1080/1351847X.2012.720269
   Web of Science ®Google Scholar
• Azzalini, A. 1985. “A Class of Distributions Which Includes the Normal Ones.” Scandinavian Journal of Statistics 12 (2):171–8.
   Web of Science ®Google Scholar
• Azzalini, A., and A. Dalla Valle. 1996. “The Multivariate Skew-Normal Distribution.” Scandinavian Journal of Statistics 13 (4):271–5.
   Google Scholar
• Bartoletti, S., and N. Loperfido. 2010. “Modelling Air Pollution Data by the Skew-Normal Distribution.” Stochastic Environmental Research and Risk Assessment 24 (4):513–7. doi:10.1007/s00477-009-0341-z
   Web of Science ®Google Scholar
• Chen, J., and A. Gupta. 2005. “Matrix Variate Skew Normal Distributions.” A Journal of Theoretical and Applied Statistics 39 (3):247–53.
   Google Scholar
• Chiang, J.-Y., T.-R. Tsai, and N.-C. Su. 2018. “Adaptive Control Charts for Skew-Normal Distribution.” Quality and Reliability Engineering International 34 (4):589–608. doi:10.1002/qre.2274
   Web of Science ®Google Scholar
• Figueiredo, F., and M. I. Gomes. 2013. “The Skew-Normal Distribution in SPC.” REVSTAT – Statistical Journal 11 (1):83–104.
   Web of Science ®Google Scholar
• Gorgin, V., and B. S. Gildeh. 2020. “Mad Control Chart for Autoregressive Models with Skew-Normal Distribution.” Stochastics and Quality Control 35 (1):17–23. doi:10.1515/eqc-2019-0006
   Google Scholar
• Gupta, A., and J. Chen. 2001. “Goodness-of-Fit Tests for the Skew-Normal Distribution.” Communications in Statistics - Simulation and Computation 30 (4):21–9.
   Web of Science ®Google Scholar
• Henze, N. 1986. “A Probabilistic Representation of the ’Skew-Normal’ Distribution.” Scandinavian Journal of Statistics 13 (4):271–5.
   Web of Science ®Google Scholar
• Li, C., A. Mukherjee, Q. Su, and M. Xie. 2019. “Some Monitoring Procedures Related to Asymmetry Parameter of Azzalini’s Skew-Normal Model.” REVSTAT – Statistical Journal 17 (1):1–24.
   Web of Science ®Google Scholar
• Li, C., N. Su, P. Su, and Y. Shyr. 2014. “The Design of and r Control Charts for Skew Normal Distributed Data.” Communications in Statistics - Theory and Methods 43 (23):4908–24. doi:10.1080/03610926.2012.717666
   Web of Science ®Google Scholar
• Lorden, G. 1970. “On Excess over the Boundary.” The Annals of Mathematical Statistics 41 (2):520–7. doi:10.1214/aoms/1177697092
   Google Scholar
• Lorden, G. 1971. “Procedures for Reacting to a Change in Distribution.” The Annals of Mathematical Statistics 42 (6):1897–908. doi:10.1214/aoms/1177693055
   Google Scholar
• Lorden, G., and M. Pollak. 1997. “Average Run Length to False Alarm for Surveillance Schemes Designed with Partially Specified Pre-Change Distribution.” The Annals of Statistics 25 (3):1284–310.
   Web of Science ®Google Scholar
• Lucito, R., J. Healy, A. Joan, R. Andrew, E. Diane, C. Maoyen, R. Linda, B. Amy, S. Jonathan, T. Jennifer, et al. 2003. “Representational Oligonucleotide Microarray Analysis: A High-Resolution Method to Detect Genome Copy Number Variation.” Genome Research 13 (10):2291–305. doi:10.1101/gr.1349003
   PubMed Web of Science ®Google Scholar
• Mei, Y. 2006. “Sequential Change-Point Detection When Unknown Parameters Are Present in the Pre-Change Distribution.” The Annals of Statistics 34 (1):92–122. doi:10.1214/009053605000000859
   Web of Science ®Google Scholar
• Moustakides, G. 1986. “Optimal Stopping Times for Detecting Changes in Distributions.” The Annuals of Statistics 14 (4):1379–87.
   Web of Science ®Google Scholar
• Ngunkeng, G., and W. Ning. 2014. “Information Approach for the Change-Point Detection in the Skew Normal Distribution and Its Applications.” Sequential Analysis 33 (4):475–90. doi:10.1080/07474946.2014.961845
   Web of Science ®Google Scholar
• Ning, W. 2014. “Probabilistic Representations of Matrix Variate Skew Normal Models.” Random Operators and Stochastic Equations 23 (1):21–9.
   Google Scholar
• Olshen, A. B., E. S. Venkatraman, R. Lucito, and M. Wigler. 2004. “Circular Binary Segmentation for the Analysis of Array-Based DNA Copy Number Data.” Biostatistics (Oxford, England) 5 (4):557–72. doi:10.1093/biostatistics/kxh008
   PubMed Web of Science ®Google Scholar
• Opperman, L., and W. Ning. 2019. “Sequential Probability Ratio Test for Skew Normal Distribution.” Sequential Analysis 50 (10):2823–36.
   Google Scholar
• Page, E. S. 1954. “Continuous Inspection Schemes.” Biometrika 41 (1-2):100–15. doi:10.1093/biomet/41.1-2.100
   Web of Science ®Google Scholar
• Pollak, M. 1987. “Average Run Lengths of an Optimal Method of Detecting a Change in Distribution.” The Annals of Statistics 15 (2):749–79. doi:10.1214/aos/1176350373
   Web of Science ®Google Scholar
• Ritov, Y. 1990. “Asymptotic Efficient Estimation of the Change Point with Unknown Distributions.” The Annuals of Statistics 18 (4):1829–39.
   Web of Science ®Google Scholar
• Roberts, S. 1966. “A Comparison of Some Control Chart Procedures.” Technometrics 8 (3):411–30. doi:10.1080/00401706.1966.10490374
   Web of Science ®Google Scholar
• Said, K., W. Ning, and Y. Tian. 2016. “Likelihood Procedure for Testing Changes in Skew Normal Model with Applications to Stock Returns.” Communications in Statistics - Simulation and Computation 46 (9):1–13.
   Web of Science ®Google Scholar
• Shiryaev, A. N. 1963. “On Optimum Methods in Quickest Detection Problems.” Theory of Probability & Its Applications 8 (1):22–46. doi:10.1137/1108002
   Google Scholar
• Siegmund, D., and E. Venkatraman. 1995. “Using the Generalized Likelihood Ratio Statistic for Sequential Detection of a Change-Point.” The Annals of Statistics 23 (1):255–71. doi:10.1214/aos/1176324466
   Web of Science ®Google Scholar
• Snijders, A. M., N. Nowak, R. Segraves, S. Blackwood, Nils Brown, J. Conroy, G. Hamilton, A. K. Hindle, B. Huey, K. Kimura, et al. 2001. “Assembly of Microarrays for Genome-Wide Measurement of DNA Copy Number.” Nature Genetics 29 (3):263–4. doi:10.1038/ng754
   PubMed Web of Science ®Google Scholar
• Tsai, T.-R. 2007. “Skew Normal Distribution and the Design of Control Charts for Averages.” International Journal of Reliability, Quality and Safety Engineering 14 (01):49–63. doi:10.1142/S0218539307002507
   Google Scholar
• Verdier, G. 2020. “An Empirical Likelihood-Based Cusum for On-Line Model Change Detection.” Communications in Statistics-Theory and Methods 49 (8):1818–39.
   Google Scholar
• Wald, A., and J. Wolfowitz. 1948. “Optimum Character of the Sequential Probability Ratio Test.” The Annals of Mathematical Statistics 19 (3):326–39. doi:10.1214/aoms/1177730197
   Google Scholar
• Xiang, D., S. Gao, W. Li, X. Pu, and W. Dou. 2019. “A New Nonparametric Monitoring of Data Streams for Changes in Location and Scale via Cucconi Statistic.” Journal of Nonparametric Statistics 31 (3):743–60. doi:10.1080/10485252.2019.1632307
   Web of Science ®Google Scholar