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Test of fit for Cauchy distribution based on the empirical likelihood ratio with application to the stock market price. (English) Zbl 1499.62151

MSC:

62G10 Nonparametric hypothesis testing
62P20 Applications of statistics to economics
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[1] Berger, J.O. and Wolpert, R.L. (1984), The Likelihood Principle. IMS Lecture Notes, Vol. 6. Institue of Mathematical Statistics, Haywood, CA. · Zbl 1060.62500
[2] D’Agostino, R.B. and Stephens, M.A. (Eds.) (1986), Goodness-of-fit Techniques, New York: Marcel Dekker. · Zbl 0597.62030
[3] Ebner, B., Eid, L., Klar, B. (2021), Cauchy or not Cauchy? New goodness-of-fit tests for the Cauchy distribution. arXiv preprint arXiv:2106.13073.
[4] Glover, S. and Dixon, P. (2004), Likelihood ratios: A simple and flexible statistic for empirical psychologists, Psychonomic Bulletin and Review, 11, 791-806.
[5] Gurevich, G. and Vexler, A. (2011), A Two-sample empirical likelihood ratio test based on samples entropy, Statistics and Computing, 21, 657-670. · Zbl 1221.62070
[6] Gurevich, G. and Vexler, A. (2018), A density based empirical likelihood approach for testing bivariate normality, Journal of Statistical Computation and Simulation, doi.org/10.1080/00949655.2018.1476516. · Zbl 07192673
[7] Johnson, N.L., Kotz, S. and Balakrishnan, N. (1994), Continuous Univariate Distributions, Wiley. ISBN 0-471-58495-9. · Zbl 0811.62001
[8] Kagan, Y.Y. (1992), Correlations of earthquake focal mechanisms, Geophys. J. Int., 110, 305-320.
[9] Kotz, S., Kozubowski, T.J. and Podg´orski, K. (2001), The Laplace distribution and generalizations: a revisit with applications to Communications, Economics, Engineering and Finance. Birkhauser. ISBN 9780817641665. · Zbl 0977.62003
[10] Lehmann, E.L. (1986), Testing Statistical Hypotheses, 2nd Edition. Springer-Verlag, New York. · Zbl 0608.62020
[11] Mahdizadeh, M. and Zamanzade, E. (2017), New goodness of fit tests for the Cauchy distribution, Journal of Applied Statistics, 44, 1106-1121. · Zbl 1516.62448
[12] Mahdizadeh, M. and Zamanzade, E. (2019), Goodness-of-fit testing for the Cauchy distribution with application to financial modeling, Journal of King Saud University - Science, 31, 1167-1174.
[13] Min, I.A., Mezic, I. and Leonard, A. (1996), Levy stable distributions for velocity and velocity difference in systems of vortex elements, Phys. Fluids, 8, 1169-1180. · Zbl 1086.76029
[14] Nolan, J.P. (2014), Financial modeling with heavy-tailed stable distributions, WIREs Comput. Stat., 6, 45-55.
[15] Shan, G., Vexler, A., Wilding, G. E. and Hutson A. D. (2011), Simple and exact empirical likelihood ratio tests for normality based on moment relations, Communications in Statistics-Simulation and Computation, 40, 141-158. · Zbl 1209.62110
[16] Shepherd, L.A., Tsai, W-M., Vexler, A. and Miecznikowski, J.C. (2013), dbEmpLikeNorm: test for joint assessment of normality, R package. Available at: http://cran.rproject.org/web/packages/dbEmpLikeNorm/index.html.
[17] Solomon, D.L. (1975), A note on the non-equivalence of the Neyman-Pearson and generalized likelihood ratio tests for testing a simple null versus a simple alternative hypothesis (PDF), The American Statistician, 29, 101-102. · Zbl 0327.62014
[18] Stapf, S. and Kimmich, R. and Seitter, R.O., Maklakov, A.I. and Skirda, V.D. (1996), Proton and deuteron fieldcycling NMR relaxometry of liquids confined in porous glasses, Coll. Surf. Physicochem. Eng. Aspects, 115, 107-114.
[19] Tanajian,H.,Vexler. A. and Hutson,A.D. (2013),Novel and efficient density based empirical likelihood procedures for symmetry and K-sample comparisons:STATA package. Available at http://sphhp.buffalo.edu/biostatistics/researchand-acilities/software/stata.html.
[20] Vexler, A. and Gurevich, G. (2010), Empirical likelihood ratios applied to goodnessof-fit tests based on sample entropy, Computational Statistics and Data Analysis, 54, 531-545. · Zbl 1464.62175
[21] Vexler, A. and Gurevich, G. (2011), A note on optimality of hypothesis testing, Mathematics in Engineering, Science and Aerospace, 2, 243-250. · Zbl 1227.62011
[22] Vexler, A. and Yu, J. (2011), Two-sample density-based empirical likelihood tests for incomplete data in application to a pneumonia study, Biometrical Journal, 53, 628-651. · Zbl 1217.62064
[23] Vexler, A., Kim, Y.M., Yu, J., Lazar, N.A. and Hutson, A.D. (2014), Computing critical values of exact tests by incorporating Monte Carlo simulations combined with statistical tables, Scandinavian Journal of Statistics, DOI: 10.1111/sjos.12079. · Zbl 1305.62183
[24] Vexler, A., Liu, S. and Schisterman, E.F. (2011c), Nonparametric likelihood inference based on cost-effectively-sampled-data, Journal of Applied Statistics, 38, 769-783. · Zbl 1511.62381
[25] Vexler, A., Shan, G., Kim, S., Tsai, W. M., L. Tian and Hutson, A. D. (2011a), An empirical likelihood ratio based goodness-of-fit test for Inverse Gaussian distributions, Journal of Statistical Planning and Inference, 141, 6, 2128-2140. · Zbl 1208.62078
[26] Vexler, A., Tsai, W-M. and Malinovsky, Y. (2012a), Estimation and testing based on data subject to measurement errors: from parametric to non-parametric likelihood methods, Statistics in Medicine, 31, 2498-2512.
[27] Vexler, A., Tsai, W-M., Gurevich, G. and Yu, J. (2012b), Two-sample density-based empirical likelihood ratio tests based on paired data, with application to a treatment study of Attention-Deficit/Hyperactivity Disorder and Severe Mood Dysregulation, Statistics in Medicine, 31, 1821-1837.
[28] Vexler, A., Yu, J. and Hutson, A.D. (2011b), Likelihood testing populations modeled by autoregressive process subject to the limit of detection in applications to longitudinal biomedical data, Journal of Applied Statistics. 38, 1333-1346. · Zbl 1218.62096
[29] Villase˜nor, J. A., Gonz´alez-Estrada, E. (2021), Goodness-of-Fit Tests for Cauchy Distributions Using Data Transformations. In Advances in Statistics-Theory and Applications (pp. 271-282). Springer, Cham.
[30] Winterton, S.S., Smy, T.J. and Tarr, N.G. (1992), On the source of scatter in contact resistance data, J. Electron. Mater., 21, 917-921.
[31] Yu, J., Vexler, A. and Tian, L. (2010), Analyzing incomplete data subject to a threshold using empirical likelihood methods: an application to a pneumonia risk study in an ICU setting, Biometrics, 66, 123-130. · Zbl 1187.62181
[32] Yu, J., Vexler, A., Kim, S. and Hutson, A. D. (2011), Two-sample empirical likelihood ratio tests for medians in application to biomarker evaluations, The Canadian Journal of Statistics. 39, 671-689. · Zbl 1228.62056
[33] Yu, J., Yang, L., Vexler, A., Hutson, A. D. (2016), A generalized empirical likelihood approach for two-group comparisons given a U-statistic constraint, Statistics: A Journal of Theoretical and Applied Statistics, 50, 435-453. · Zbl 1359.62153
[34] Zhang, J. (2002), Powerful goodness-of-fit tests based on the likelihood ratio, Journal of Royal Statistical Society, Series B, 64, 281-294. · Zbl 1067.62046
[35] Zhao, Y., Vexler, A., Hutson, A., Chen, X. (2017), A statistical software procedure for exact parametric and nonparametric likelihood-ratio tests for two-sample comparisons, Communications in Statistics - Simulation and Computation, 46, 2829-2841 · Zbl 1373.62204
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