Communications for Statistical Applications and Methods

  • 제29권3호
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  • Pages.301-317
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  • 2022
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  • 2287-7843(pISSN)
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  • 2383-4757(eISSN)
한국통계학회 (The Korean Statistical Society)
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Modified information criterion for testing changes in generalized lambda distribution model based on confidence distribution

  • Ratnasingam, Suthakaran (Department of Mathematics, California State University San Bernardino) ;
  • Buzaianu, Elena (Department of Mathematics and Statistics, University of North Florida) ;
  • Ning, Wei (Department of Mathematics and Statistics, Bowling Green State University)
  • 투고 : 2021.09.25
  • 심사 : 2021.11.22
  • 발행 : 2022.05.31
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초록

In this paper, we propose a change point detection procedure based on the modified information criterion in a generalized lambda distribution (GLD) model. Simulations are conducted to obtain empirical critical values of the proposed test statistic. We have also conducted simulations to evaluate the performance of the proposed methods comparing to the log-likelihood method in terms of power, coverage probability, and confidence sets. Our results indicate that, under various conditions, the proposed method modified information criterion (MIC) approach shows good finite sample properties. Furthermore, we propose a new goodness-of-fit testing procedure based on the energy distance to evaluate the asymptotic null distribution of our test statistic. Two real data applications are provided to illustrate the use of the proposed method.

키워드

과제정보

The authors would like to thank three anonymous reviewers for their constructive comments and suggestions, which helped improve this manuscript significantly.

참고문헌

  1. Baringhaus L and Franz C (2004). On a new multivariate two-sample test, Journal of Multivariate Analysis, 88, 190-206. https://doi.org/10.1016/S0047-259X(03)00079-4
  2. Cunen C, Hermansen G, and Hjort NL (2018). Confidence distributions for change-points and regime shifts, Journal of Statistical Planning and Inference, 195, 14-34. https://doi.org/10.1016/j.jspi.2017.09.009
  3. Chen J, Gupta AK, and Pan J (2006). Information criterion and change point problem for regular models, The Indian Journal of Statistics, 68, 252-282.
  4. Karian ZA and Dudewicz EJ (2000). Fitting Statistical Distributions, The Generalized Lambda Distribution and Generalized Bootstrap Methods, Boca Raton, CRC Press.
  5. Kim AY, Marzban C, Percival DB, and Stuetzle W (2009). Using labeled data to evaluate change detectors in a multivariate streaming environment, Signal Processing, 89, 2529-2536. https://doi.org/10.1016/j.sigpro.2009.04.011
  6. Matteson DS and James NA (2014). A nonparametric approach for multiple change point analysis of multivariate data, Journal of the American Statistical Association, 109, 334-345. https://doi.org/10.1080/01621459.2013.849605
  7. Ngunkeng G and Ning W (2014). Information approach for the change-point detection in the skew normal distribution and its applications, Sequential Analysis, 33, 475-490. https://doi.org/10.1080/07474946.2014.961845
  8. Ning W and Gupta AK (2009). Change point analysis for generalized lambda distribution, Communications in Statistics-Simulation and Computation, 38, 1789-1802. https://doi.org/10.1080/03610910903125314
  9. Pearson K (1985). Contributions to the mathematical theory of evolution, Philisophical Transactions of the Royal Society of London A, 185, 71-110.
  10. Ramberg JS and Schmeiser BW (1972). An approximate method for generating symmetric random variables, Communications of the ACM, 15, 987-990. https://doi.org/10.1145/355606.361888
  11. Ramberg JS and Schmeiser BW (1974). An approximate method for generating asymmetric random variables, Communications of the ACM , 17, 78-82. https://doi.org/10.1145/360827.360840
  12. Ramberg JS, Tadikamalla PR, Dudewicz EJ, and Mykytka EF (1979). A probability distribution and its uses in fitting data, Technometrics, 21, 201-204. https://doi.org/10.1080/00401706.1979.10489750
  13. Ratnasingam S and Ning W (2020). Confidence distributions for skew normal change-point model based on modified information criterion, Journal of Statistical Theory and Practice, 4, 1-21. https://doi.org/10.1080/15598608.2010.10411970
  14. Ratnasingam S and Ning W (2021). Modified information criterion for regular change point models based on confidence distribution, Environmental and Ecological Statistics, 28, 303-322. https://doi.org/10.1007/s10651-021-00485-5
  15. Rizzo ML (2002). A new rotation invariant goodness-of-fit test (PhD thesis), Bowling Green State University.
  16. Rizzo ML (2009). New goodness-of-Fit tests for Pareto distributions, Journal of the International Association of Actuaries, 39, 691-715.
  17. Rizzo ML and Haman JT (2016). Expected distances and goondess-of-fit for the asymmetric Laplace distribution, Statistics and Probability Letters, 117, 158-164. https://doi.org/10.1016/j.spl.2016.05.006
  18. Schweder T and Hjort N (2002). Confidence and likelihood, Scandinavian Journal of Statistics, 29, 309-332. https://doi.org/10.1111/1467-9469.00285
  19. Schweder T and Hjort NL (2016). Confidence, Likelihood, Probability: Statistical Inference with Confidence Distributions, Cambridge University Press.
  20. Shen J, Liu R, and Xie M (2018). Prediction with confidence-a general framework for predictive inference, Journal of Statistical Planning and Inference, 195, 126-140. https://doi.org/10.1016/j.jspi.2017.09.012
  21. Singh K, Xie M, and Strawderman WE (2005). Combining information from independent sources through confidence distributions, Annals of Statistics, 33, 159-183. https://doi.org/10.1214/009053604000001084
  22. Singh K, Xie M, and Strawderman WE (2007). Confidence distribution (cd): distribution estimator of a parameter, Lecture Notes-Monograph Series Complex Datasets and Inverse Problems: Tomography, Networks and Beyond, 54, 132-150.
  23. Singh K and Xie M (2012). CD posterior-combining prior and data through confidence distributions, Contemporary Developments in Bayesian Analysis and Statistical Decision Theory: A Festchrift in Honor of Williams E. Strawderman (D. Fourdrinier et al. eds.), IMS Collection, 8, 200-214.
  24. Su S (2016). Fitting flexible parametric regression models with GLDreg in R, Journal of Modern Applied Statistical Methods, 15.
  25. Szekely GJ (2000). Technical report 03-05: E-statistics: energy of statistical samples, Department of Mathematics and Statistics, Bowling Green State University.
  26. Szekely GJ and Rizzo ML (2004). Testing for equal distributions in high dimension, Mathematics, 1-6.
  27. Szekely GJ and Rizzo ML (2005). A new test for multivariate normality, Journal of Multivariate Analysis, 93, 58-80. https://doi.org/10.1016/j.jmva.2003.12.002
  28. Szekely GJ and Rizzo ML (2013). Energy statistics: A class of statistics based on distances, Journal of Statistical Planning and Inference, 143, 1249--1272. https://doi.org/10.1016/j.jspi.2013.03.018
  29. Tukey JW (1960). The Practical Relationship Between the Common Transformations of Percentages of Counts and of AmountsTukey, J. W., Technical Reports, 36, Statistical Techniques Research Group, Princeton University.
  30. Vostrikova (1981). Detecting "disorder" in multidimensional random processes, Soviet Mathematics Doklady, 24, 55-59.
  31. Xie M and Singh K (2013). Confidence distribution, the frequentist distribution estimator of a parameter: A review, International Statistical Review, 81, 2-39. https://doi.org/10.1111/insr.12013
  32. Yang G (2012). The energy goodness-of-fit test for univariate stable distributions (PH. D Thesis), Bowling Green State University.