آزمون خودگردان برای فرض تقارن بر اساس آنتروپی‌ تجمعی

نوع مقاله: مقاله پژوهشی

نویسنده

گروه آمار، دانشگاه محقق اردبیلی

چکیده

چکیده: فرض متقارن بودن توزیع احتمالی متغیر موردمطالعه، از فرضیات محوری در روش‌های استنباط آماری بخصوص در روش‌های ناپارامتری است. بر اساس معیارهای گوناگون انحراف از تقارن، آماره‌های آزمون مختلفی برای آزمون این فرض ارائه‌شده است. در این مقاله بر اساس آنتروپی تجمعی معیار جدیدی برای چولگی معرفی‌شده و بر مبنای آن ‌آزمونی برای فرض تقارن ارائه می‌شود که در آن p- مقدار آزمون با استفاده از روش خودگردان محاسبه می‌گردد. از شبیه‌سازی کامپیوتری برای ارزیابی عملکرد آماره آزمون ارائه‌شده و مقایسه توان آن با توان آزمون‌های رقیب استفاده‌شده است.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

A Bootstrap Test for Symmetry based on Cumulative Entropy

نویسنده [English]

  • Vali Zardasht
Department of Statistics, University of Mohaghegh Ardabili, Ardabil, Iran
چکیده [English]

The symmetry assumption plays an important role in nonparametric statistical inference methods. Using different measure of asymmetry, various test statistics has proposed for testing the symmetry hypothesis. In this paper, we apply the cumulative residual entropy to introduce a new skewness measure and construct a distribution–free test for the hypothesis. Bootstrap re-sampling from a symmetric empirical distribution function is used to calculate the p-value of the test. The power of the new test statistic is compared with two existing tests in a simulation study. The results show that the proposed test preserves its level and it has reasonable power properties on the family of distribution evaluated.

کلیدواژه‌ها [English]

  • symmetry
  • Entropy measures
  • Inaccuracy measure
  • Skewness measure
  • Bootstrap
[1] Lehmann, E.L. and Romano, J.P. (2005). Testing Statistical Hypotheses, New York: Springer.

[2] Yoshizawa, C.N. (1984). Some Tests of Symmetry, Department of Biostatistics University of North Carolina at Chapel Hill Institute of Statistics Mimeo Series No. 1460.

[3] Miao, W., Gel, Y. R., and Gastwirth, J. L. (2006). A New Test of Symmetry about an Unknown Median. Random Walk, Sequential Analysis and Related Topics - A Festschrift in Honor of Yuan-Shih Chow. Eds.: Agnes Hsiung, Cun-Hui Zhang, and Zhiliang Ying, World Scientific Publisher, Singapore.

[4] Cabilio P. and Masaro, J. (1996). A simple test of symmetry about an unknown median, Canadian Journal of Statistics, 24, 349–361.

[5] Mira A. (1999). Distribution-free test for symmetry based on Bonferroni’s measure, Journal of Applied Statistics, 26, 959–972.

[6] Shannon, C.E. (1948). A mathematical theory of communication, Bell System Technical Journal, 27, 279–423.

[7] Rao, M., Chen, Y., Vemuri, B.C. and Wang, F. (2004). Cumulative residual entropy: a new measure of information, IEEE Transactions on Information Theory, 50, 1220–1228.

[8] Di Crescenzo, A. and Longobardi, M. (2009). On cumulative entropies, Journal of Statistical Planning and Inference, 139, 4072-4087.

[9] Rao, M. (2005). More on a new concept of entropy and information, Journal of Theoretical Probability, 18, 967–981.

[10] Asadi, M. and Zohrevand, Y. (2007). On the dynamic cumulative residual entropy, Journal of Statistical Planning and Inference, 137, 1931–1941.

[11] Navarro, J., del Aguila, Y., and Asadi, M. (2010). Some new results on the cumulative residual entropy, Journal of Statistical Planning and Inference, 140, 310-322.

[12] Drissi, N., Chonavel, T. and Boucher, J.M. (2008). Generalized Cumulative Residual Entropy for Distributions with Unrestricted Supports, Hindawi Publishing Corporation doi:10.1155/2008/790607.

[13] Kerridge, D. F. (1961). Inaccuracy and inference, Journal of Royal Statistical Society, Series B, 23, 184-194.

[14] Kundu, C., Di Crescenzo, A. and Longobardi, M. (2016). On cumulative residual (past) inaccuracy for truncated random variables, Metrika, 79(3), 335-356.

[15] Taneja, H.C. and Kumar, V. (2012). On dynamic cumulative residual inaccuracy measure. In Ao S.I. et al. (eds.), Proceedings of the World Congress on Engineering, 1, London, U.K., 153-156.

[16] Modarres R. (2002). Efficient nonparametric estimation of a distribution function, Computational Statistics and Data Analysis, 39, 75–95.

[17] Zheng, T.and Gastwirth, J.L. (2010). On Bootstrap Tests of Symmetry About an Unknown Median, Journal of Data Science, 8, 413–427.

[18] Ghosh, K. A. (2011). New Nonparametric Test of Symmetry, Advances inDirectional and Linear Statistics. Wells, M. T. and A. SenGupta (eds.), Springer-Verlag Berlin Heidelberg, 69-83.