Yıl 2018, Cilt 47, Sayı 4, Sayfalar 1061 - 1069 2018-08-01

A bootstrap test for symmetry based on quantiles

Vali Zardasht [1]

11 22

In this paper, we construct a nonparametric test for the symmetry assumption of an underling distribution based on the sample quantiles. Bootstrap re-sampling from a symmetric empirical distribution function is used to obtain the p-value of the test. The power of the new test statistic is compared with some well-known symmetry tests using 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.
Symmetry, Quantile, Test Power, Bootstrap, Simulation
  • Cabilio, P. and Masaro, J. A simple test of symmetry about an unknown median, Canadian Journal of Statistics 24, 349-361, 1996.
  • Drikvandi, R., Modarres, R. and Jalilian, A. H. A bootstrap test for symmetry based on ranked set samples, Computational Statistics and Data Analysis 55, 1807-1814, 2011.
  • Gupta, M. K. An asymptotically nonparametric test of symmetry, The Annals of Mathe- matical Statistics 38(3), 849-866, 1967.
  • Huber, P. J. Robust statistics: A review, The Annals of Mathematical Statistics 43, 1041 1067, 1972.
  • Meintanis, S.G. and Ngatchou-Wandji, J. Recent tests for symmetry with multivariate and structured data, in: Jiang, J., Roussas, G. G. and Samaniego, F. J. (Eds.), Non-Parametric Statistical Methods and Related Topics: A Festschrift in honor of Professor P.K. Bhat- tacharya on the occasion of his 80th birthday (World Scientic, New Jersey, 2012,) 35-73.
  • Miao, W., Gel, Y. R., and Gastwirth, J. L. 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 Scien- tic Publisher, 2006).
  • Mira, A. Distribution-free test for symmetry based on Bonferroni's measure, Journal of Applied Statistics 26, 959-972, 1999.
  • Modarres, R. Efficient nonparametric estimation of a distribution function, Computational Statistics and Data Analysis 39, 75-95, 2002.
  • Munzel, U. Nonparametric methods for paired samples, Statistica Neerlandica 53, 277-286, 1999.
  • Ngatchou- Wandji, J. On testing for the nullity of some skewness coefficients, International Statatistics Review 74, 47-65, 2006.
  • Sering, R. J. Approximation Theorems of Mathematical Statistics (John Wiley and Sons Inc, 1980).
  • Staudte, R. G. Inference for quantile measures of skewness, TEST 23, 751-768, 2014.
  • Taylor, H. M. and Karlin, S. An Introduction to Stochastic Modeling (Academic Press, 1998).
  • Van der vaart, A. W. Asymptotic statistics (Cambridge University Press, 1998).
  • Zheng, T. and Gastwirth, J.L. On Bootstrap Tests of Symmetry About an Unknown Median, Journal of Data Science 8(3), 413-427, 2010.
Birincil Dil en
Konular Matematik ve İstatistik
Dergi Bölümü İstatistik
Yazarlar

Yazar: Vali Zardasht (Sorumlu Yazar)

Bibtex @araştırma makalesi { hujms453625, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {1303-5010}, address = {Hacettepe Üniversitesi}, year = {2018}, volume = {47}, pages = {1061 - 1069}, doi = {}, title = {A bootstrap test for symmetry based on quantiles}, key = {cite}, author = {Zardasht, Vali} }
APA Zardasht, V . (2018). A bootstrap test for symmetry based on quantiles. Hacettepe Journal of Mathematics and Statistics, 47 (4), 1061-1069. Retrieved from http://dergipark.gov.tr/hujms/issue/38872/453625
MLA Zardasht, V . "A bootstrap test for symmetry based on quantiles". Hacettepe Journal of Mathematics and Statistics 47 (2018): 1061-1069 <http://dergipark.gov.tr/hujms/issue/38872/453625>
Chicago Zardasht, V . "A bootstrap test for symmetry based on quantiles". Hacettepe Journal of Mathematics and Statistics 47 (2018): 1061-1069
RIS TY - JOUR T1 - A bootstrap test for symmetry based on quantiles AU - Vali Zardasht Y1 - 2018 PY - 2018 N1 - DO - T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1061 EP - 1069 VL - 47 IS - 4 SN - 1303-5010- M3 - UR - Y2 - 2016 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics A bootstrap test for symmetry based on quantiles %A Vali Zardasht %T A bootstrap test for symmetry based on quantiles %D 2018 %J Hacettepe Journal of Mathematics and Statistics %P 1303-5010- %V 47 %N 4 %R %U
ISNAD Zardasht, Vali . "A bootstrap test for symmetry based on quantiles". Hacettepe Journal of Mathematics and Statistics 47 / 4 (Ağustos 2018): 1061-1069.