References
- Aitchison, J. 2003. The statistical analysis of compositional data. Caldwell, NJ: Blackburn Press.
- Barndorff-Nielsen, O. E. 1986. Inference on full or partial parameters, based on the standardized signed log likelihood ratio. Biometrika 73:307–22. doi:https://doi.org/10.2307/2336207.
- Barndorff-Nielsen, O. E. 1991. Modified signed log likelihood ratio. Biometrika 78 (3):557–63. doi:https://doi.org/10.1093/biomet/78.3.557.
- Barndorff-Nielsen, O. E., and D. R. Cox. 1984. Bartlett adjustment to the likelihood ratio statistic and the distribution of maximum likelihood estimator. Journal of the Royal Statistical Society B 46:483–95. doi:https://doi.org/10.1111/j.2517-6161.1984.tb01321.x.
- Barndorff-Nielsen, O. E., and P. Hall. 1988. On the level-error after Bartlett adjustment of the likelihood ratio statistic. Biometrika 75 (2):374–8. doi:https://doi.org/10.1093/biomet/75.2.374.
- Bayer, F. M., and F. Cribari-Neto. 2013. Bartlett corrections in beta regression models. Journal of Statistical Planning and Inference 143 (3):531–47. doi:https://doi.org/10.1016/j.jspi.2012.08.018.
- Bierens, H. 1994. Topics in advanced econometrics. Cambridge, UK: Cambridge University Press.
- Cordeiro, G. M. 1993. General matrix formulae for computing Bartlett corrections. Statistics and Probability Letters 16 (1):11–8. doi:https://doi.org/10.1016/0167-7152(93)90115-Y.
- Cordeiro, G. M., and F. Cribari-Neto. 2014. An introduction to Bartlett correction and bias reduction. New York, NY: Springer.
- Doornik, J. A. 2013. Object-oriented matrix programming using ox. London, UK: Timberlake Consultants Press.
- Efron, B. 1987. Better bootstrap confidence intervals. Journal of the American Statistical Association 82 (397):171–85. doi:https://doi.org/10.1080/01621459.1987.10478410.
- Efron, B., and R. J. Tibshirani. 1993. An introduction to the bootstrap. New York, NY: Chapman and Hall.
- Ferrari, S. L. P., and A. H. M. A. Cysneiros. 2008. Skovgaard’s adjustment to likelihood ratio tests in exponential family nonlinear models. Statistics and Probability Letters 78 (17):3047–55. doi:https://doi.org/10.1016/j.spl.2008.05.009.
- Ferrari, S. L. P., and E. C. Pinheiro. 2011. Improved likelihood inference in beta regression. Journal of Statistical Computation and Simulation 81 (4):431–43. doi:https://doi.org/10.1080/00949650903389993.
- Krätschmer, V. 2007. The uniqueness of extremum estimation. Statistics and Probability Letters 77 (10):942–51. doi:https://doi.org/10.1016/j.spl.2006.12.009.
- Kotz, S., B. Balakrishnan, and N. L. Johnson. 2000. Continuous multivariate distributions. Vol. 1, 2nd ed. New York, NY: John Wiley & Sons.
- Lawley, D. 1956. A general method for approximating to the distribution of likelihood ratio criteria. Biometrika 43 (3–4):295–303. doi:https://doi.org/10.1093/biomet/43.3-4.295.
- Maier, M. J. 2013. DirichletReg: Dirichlet Regression in R. R package version 0.6-3. https://cran.r-project.org/web/packages/DirichletReg/.
- Maier, M. J. 2014. DirichletReg: Dirichlet Regression for Compositional Data in R. Research Report Series/Department of Statistics and Mathematics, 125. WU Vienna University of Economics and Business, Vienna.
- Melo, T. F. N., K. L. P. Vasconcellos, and A. J. Lemonte. 2009. Some restriction tests in a new class of regression models for proportions. Computational Statistics and Data Analysis 53 (12):3972–9. doi:https://doi.org/10.1016/j.csda.2009.06.005.
- Noma, H., K. Nagashima, K. Maruo, M. Gosho, and T. A. Furukawa. 2018. Bartlett-type corrections and bootstrap adjustments of likelihood-based inference methods for network meta-analysis. Statistics in Medicine 37 (7):1178–90. doi:https://doi.org/10.1002/sim.7578.
- Core Team, R. 2016. R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing.
- Rocke, D. M. 1989. Bootstrap Bartlett adjustment in seemingly unrelated regression. Journal of the American Statistical Association 84 (406):598–601. doi:https://doi.org/10.1080/01621459.1989.10478809.
- Scott, D. W. 1979. On optimal and data-based histograms. Biometrika 66 (3):605–10. doi:https://doi.org/10.1093/biomet/66.3.605.
- Shutoh, N., T. Nishiyama, and M. Hyodo. 2017. Bartlett correction to the likelihood ratio test for MCAR with two-tep monotone sample. Statistica Neerlandica 71 (3):184–99. doi:https://doi.org/10.1111/stan.12106.
- Skovgaard, I. M. 1996. An explicit large-deviation approximation to one-parameter tests. Bernoulli 2 (2):145–65. doi:https://doi.org/10.2307/3318548.
- Skovgaard, I. M. 2001. Likelihood asymptotics. Scandinavian Journal of Statistics 28 (1):3–32. doi:https://doi.org/10.1111/1467-9469.00223.
- van Giersbergen, N. P. A. 2009. Bartlett correction in the stable AR(1) model with intercept and trend. Econometric Theory 25 (3):857–72. doi:https://doi.org/10.1017/S0266466609090690.