References
- Akaike, H. 1974. A new look at the statistical model identification. IEEE Transactions on Automatic Control 19 (6):716–723. doi:https://doi.org/10.1109/TAC.1974.1100705.
- Aristodemou, K. 2014. New regression methods for measures of central tendency. Ph.D. thesis. In School of Information Systems. Brunel University: Computing and Mathematics.
- Atkinson, A. C. 1981. Two graphical displays for outlying and influential observations in regression. Biometrika 68 (1):13–20. doi:https://doi.org/10.1093/biomet/68.1.13.
- Chen, Y.-C. 2018. Modal regression using kernel density estimation: A review. Wiley Interdisciplinary Reviews: Computational Statistics 10 (4):e1431. doi:https://doi.org/10.1002/wics.1431.
- Chen, Y., Genovese, C. R., Tibshirani, R. J. and Wasserman, L. et al. 2016. Nonparametric modal regression. The Annals of Statistics. 44(2):489–514. doi:https://doi.org/10.1214/15-AOS1373.
- Core Team, R. 2020. R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. https://www.R-project.org/.
- Cox, D. R., and D. V. Hinkley. 1974. Theoretical Statistics. London: Chapman & Hall/CRC.
- Dunn, P. K., and G. K. Smyth. 1996. Randomized quantile residuals. Journal of Computational and Graphical Statistics 5 (3):236–244.
- Ghitany, M. E., J. Mazucheli, A. F. B. Menezes, and F. Alqallaf. 2019. The unit-Inverse-Gaussian distribution: A new alternative to two-parameter distributions on the unit interval. Communications in Statistics - Theory and Methods 48 (14):3423–3438. doi:https://doi.org/10.1080/03610926.2018.1476717.
- Grassia, A. 1977. On a family of distributions with argument between 0 and 1 obtained by transformation of the Gamma distribution and derived compound distributions. Australian Journal of Statistics 19 (2):108–114. doi:https://doi.org/10.1111/j.1467-842X.1977.tb01277.x.
- Gupta, R. D., and D. Kundu. 1999. Generalized exponential distributions. Australian New Zealand Journal of Statistics 41 (2):173–188. doi:https://doi.org/10.1111/1467-842X.00072.
- Hartigan, P. M. 1985. Algorithm as 217: Computation of the dip statistic to test for unimodality. Journal of the Royal Statistical Society. Series C (Applied Statistics) 34 (3):320–325.
- Jones, M. 2009. Kumaraswamy’s distribution: A beta-type distribution with some tractability advantages. Statistical Methodology 6 (1):70–81. doi:https://doi.org/10.1016/j.stamet.2008.04.001.
- Korosteleva, O. 2019. Advanced Regression Models with SAS and R. Taylor & Francis Group: CRC Press.
- Kumaraswamy, P. 1980. A generalized probability density function for double-bounded random processes. Journal of Hydrology 46 (1–2):79–88. doi:https://doi.org/10.1016/0022-1694(80)90036-0.
- Lee, M. 1989. Mode regression. Journal of Econometrics 42 (3):337–349. doi:https://doi.org/10.1016/0304-4076(89)90057-2.
- Mazucheli, J., A. F. Menezes, and S. Dey. 2019a. Unit-gompertz distribution with applications. Statistica 79 (1):25–43.
- Mazucheli, J., A. F. B. Menezes, L. B. Fernandes, R. P. Oliveira, and M. E. Ghitany. 2020b. The unit-Weibull distribution as an alternative to the Kumaraswamy distribution for the modeling of quantiles conditional on covariates. Journal of Applied Statistics 47 (6):954–974. doi:https://doi.org/10.1080/02664763.2019.1657813.
- Mazucheli, J., A. F. B. Menezes, and M. E. Ghitany. 2018c. The unit-Weibull distribution and associated inference. Journal of Applied Probability and Statistics 13 (2):1–22.
- Mazucheli, J., A. F. B. Menezes, and S. Chakraborty. 2019b. On the one parameter unit-Lindley distribution and its associated regression model for proportion data. Journal of Applied Statistics 46 (4):700–714. doi:https://doi.org/10.1080/02664763.2018.1511774.
- Mazucheli, J., A. F. B. Menezes, and S. Dey. 2018a. Improved maximum-likelihood estimators for the parameters of the unit-gamma distribution. Communications in Statistics - Theory and Methods 47 (15):3767–3778. doi:https://doi.org/10.1080/03610926.2017.1361993.
- Mazucheli, J., A. F. B. Menezes, and S. Dey. 2018b. The unit-Birnbaum-Saunders distribution with applications. Chilean Journal of Statistics 9 (1):47–57.
- Mazucheli, J., S. R. Bapat, and A. F. B. Menezes. 2020a. A new one-parameter unit-Lindley distribution. Chilean Journal of Statistics 11 (1):53–67.
- Oliveira, R. P., A. F. B. Menezes, J. Mazucheli, and J. A. Achcar. 2019. Mixture and nonmixture cure fraction models assuming discrete lifetimes: Application to a pelvic sarcoma dataset. Biometrical Journal 61 (4):813–826. doi:https://doi.org/10.1002/bimj.201800030.
- Pan, Y., E. Imani, M. White, and A.-M. Farahmand. 2020. An implicit function learning approach for parametric modal regression. arXiv Preprint arXiv 2002:06195.
- Pereira, T. L., and F. Cribari-Neto. 2014. Detecting model misspecification in inflated beta regressions. Communications in Statistics - Simulation and Computation 43 (3):631–656. doi:https://doi.org/10.1080/03610918.2012.712183.
- Ramsey, J. B. 1969. Tests for specification errors in classical linear least-squares regression analysis. Journal of the Royal Statistical Society: Series B (Methodological) 31 (2):350–371. doi:https://doi.org/10.1111/j.2517-6161.1969.tb00796.x.
- Sager, T. W., and R. A. Thisted. 1982. Maximum likelihood estimation of isotonic modal regression. The Annals of Statistics 10 (3):690–707. doi:https://doi.org/10.1214/aos/1176345865.
- Smithson, M., and J. Verkuilen. 2006. A better lemon squeezer? Maximum-likelihood regression with beta-distributed dependent variables. Psychological Methods 11 (1):54–71. doi:https://doi.org/10.1037/1082-989X.11.1.54.
- Vuong, Q. H. 1989. Likelihood ratio tests for model selection and non-nested hypotheses. Econometrica 57 (2):307–333. doi:https://doi.org/10.2307/1912557.
- Wang, X., H. Chen, W. Cai, D. Shen, and H. Huang, 2017. Regularized modal regression with applications in cognitive impairment prediction. In: Advances in neural information processing systems.
- Yao, W., and L. Li. 2014. A new regression model: Modal linear regression. Scandinavian Journal of Statistics 41 (3):656–671. doi:https://doi.org/10.1111/sjos.12054.
- Zhou, H., and X. Huang; for the Alzheimer’s Disease Neuroimaging Initiative. 2020. Parametric mode regression for bounded responses. Biometrical Journal 62 (7):1791–1809. doi:https://doi.org/10.1002/bimj.202000039.