Estimating Box-Cox power transformation parameter via goodness-of-fit tests

References

• Anderson, T. W., Darling, D. A. ( 1954). A test of goodness of fit. Journal of the American Statistical Association 49(268):765–769.
   Web of Science ®Google Scholar
• Barrios, E. ( 2012). BHH2: Useful Functions for Box, Hunter and Hunter II. R package version 2012.04-0; available at http://CRAN.R-project.org/package=BHH2.
   Google Scholar
• Benjamini, Y., Hochberg, Y. ( 1995). Controlling the false discovery rate: A practical and powerful approach to multiple testing. Journal of the Royal Statistical Society—Statistical Methodology 57:289–300.
   Web of Science ®Google Scholar
• Benjamini, Y., Yekutieli, D. ( 2001). The control of the false discovery rate in multiple testing under dependency. Annals of Statistics 29:1165–1188.
   Web of Science ®Google Scholar
• Box, G. E. P., Cox, D. R. ( 1964). An analysis of transformations (with discussion). Journal of the Royal Statistical Society—Statistical Methodology 26:211–252.
   Web of Science ®Google Scholar
• Burton, B., Altman, D. G., Royston, P., Holder R. L. ( 2006). The design of simulation studies in medical statistics. Statistics in Medicine 25:4279–4292.
   PubMed Web of Science ®Google Scholar
• Cramer, H. ( 1928). On the composition of elementary errors. Scandinavian Actuarial Journal 11:141–180.
   Google Scholar
• Dag, O., Asar, O., Ilk, O. ( 2014). A methodology to implement Box-Cox transformation when no covariate is available. Communications in Statistics—Simulation and Computation 43(7):1749–1759.
   Web of Science ®Google Scholar
• Gillard, J. ( 2012). A generalised Box–Cox transformation for the parametric estimation of clinical reference intervals. Journal of Applied Statistics 39(10):2231–2245.
   Web of Science ®Google Scholar
• Jarque, C. M., Bera, A. K. ( 1987). A test for normality of observations and regression residuals. International Statistical Revivew 55(2):163–172.
   Web of Science ®Google Scholar
• Lee, M. H., Sadaei, H. J. , Suhartono ( 2013). Improving TAIEX forecasting using fuzzy time series with Box–Cox power transformation. Journal of Applied Statistics 40:2407–2422.
   Web of Science ®Google Scholar
• Lilliefors, H. W. ( 1967). On the Kolmogorov-Smirnov test for normality with mean and variance unknown. Journal of the American Statisical Association. 62:399–402.
   Web of Science ®Google Scholar
• MATLAB - The Language of Technical Computing, Version 7.10.0 (R2010a); The MathWorks Inc., Natick, Massachusetts; available at http://www.mathworks.com/products/matlab/.
   Google Scholar
• Noughabi, H. A., Arghami, N. R. ( 2011). Monte Carlo comparison of seven normality tests. Journal of Statistical Computation and Simulation 81(8):965–972.
   Web of Science ®Google Scholar
• R Development Core Team ( 2013). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria, available at http://www.R-project.org/, 2013.
   Google Scholar
• Pearson, K. ( 1900). On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling. Philosophical Magazine Series 550(302):157–175.
   Google Scholar
• Rahman, M. ( 1999). Estimating the Box-Cox transformation via Shapiro-Wilk W Statistic. Communications in Statistics—Simulation and Computation 28(1):223–241.
   Web of Science ®Google Scholar
• Rahman, M., Pearson, L. M. ( 2008). Anderson-Darling statistic in estimating the Box-Cox transformation parameter. Journal of Applied Probability & Statistics 3(1):45–57.
   Google Scholar
• Romano, J. P., Shaikh, A. M., Wolf, M. ( 2010). Multiple testing. In: Steven N. Durlauf, Lawrence E. Blume, eds. The New Palgrave Dictionary of Economics Online. Palgrave Macmillan; available at http://www.dictionaryofeconomics.com/article?id=pde2010_M000425.
   Google Scholar
• Shapiro, S. S., Francia, R. S. ( 1972). Approximate analysis of variance test for normality. Journal of the American Statistical Association 67:215–216.
   Web of Science ®Google Scholar
• Shapiro, S. S., Wilk, M. B. ( 1965). An analysis of variance test for normality (complete samples). Biometrika 52(3/4):591–611.
   Web of Science ®Google Scholar
• Sinharay, S., Stern, H. S., Russell, D. ( 2001). The use of multiple imputation for the analysis of missing data. Psychological Methods 6:317–329.
   PubMed Web of Science ®Google Scholar
• Sun, L., Tong, X., Zhou, X. ( 2011). A class of Box-Cox transformation models for recurrent event data. Lifetime Data Analysis 17: 280–301.
   PubMed Web of Science ®Google Scholar
• T. Thadewald, T., Buning, H. ( 2007). Jarque-Bera test and its competitors for testing normality—a power comparison. Journal of Applied Statistics 34(1):87–105.
   Web of Science ®Google Scholar
• Thode, H. C. ( 2002). Testing For Normality. New York: Marcel Dekker.
   Google Scholar
• Weisberg, S., Bingham, C. ( 1975). An approximate analysis of variance test for non-normality suitable for machine calculation. Technometrics 17:133–134.
   Web of Science ®Google Scholar
• Yap, B. W., Sim, C. H. ( 2011). Comparisons of various types of normality tests. Journal of Statistical Computation and Simulation 81(12):2141–2155.
   Web of Science ®Google Scholar