A new family of quantile regression models applied to nutritional data

References

• H. Akaike, A new look at the statistical model identification, IEEE Trans. Automatic Control 19 (1974), pp. 716–723.
   Web of Science ®Google Scholar
• B.C. Arnold and R.A. Groeneveld, Measures skewness with respect to the mode, The Amer. Statist. 49 (2008), pp. 34–38.
   Google Scholar
• A. Azzalini, A class of distributions which includes the normal ones, Scand. J. Statist. 12 (1985), pp. 171–178.
   Web of Science ®Google Scholar
• R.J. Barlow, Statistics: A Guide to the Use of Statistical Methods in the Physical Sciences, Wiley, Chichester, 1993.
   Google Scholar
• M. Bourguignon, J. Leão, and D.I. Gallardo, Parametric modal regression with varying precision, Biometrical J. 62 (2020), pp. 202–220.
   PubMed Web of Science ®Google Scholar
• R.D. Cook, Assessment of local influence, J. Royal Statist. Soci.: Ser. B. 48 (1986), pp. 133–155.
   Google Scholar
• R.D. Cook and S. Weisberg, Residuals and Influence in Regression, Chapman & Hall, New York, 1982.
   Google Scholar
• D. Cox and D. Hinkley, Theoretical Statistics, Chapman & Hall, London, 1974.
   Google Scholar
• D.R. Cox and E.J. Snell, A general definition of residuals, J. Royal Statist. Soc.: Ser. B. 30 (1968), pp. 248–275.
   Google Scholar
• C. Davino, M. Furno, and D. Vistocco, Quantile Regression: Theory and Applications, Wiley, Chichester, 2013.
   Google Scholar
• N.R. Draper and H. SmithApplied Regression Analysis, Wiley, New York, 1998.
   Google Scholar
• P.K. Dunn and G.K. Smyth, Randomized quantile residuals, J. Comput. Graphical Statist. 5 (1996), pp. 236–244.
   Google Scholar
• J. Elsamma and K. Jayakumar, Skew Cauchy distribution and process, J. Statist. Appl. 7 (2012), pp. 15–28.
   Google Scholar
• C.E. Galarza, L. Benites, V.H. Lachos, and M.C.E. Galarza, Package ‘lqr’, 2015.
   Google Scholar
• C.E. Galarza, V.H. Lachos, C. Barbosa, and L.M. Castro, Robust quantile regression using a generalized class of skewed distributions, Stat 6 (2017), pp. 113–130.
   Web of Science ®Google Scholar
• D.I. Gallardo, M. Bourguignon, C.E. Galarza, and H.W. Gómez, A parametric quantile regression model for asymmetric response variables on the real line, Symmetry 12 (2020), pp. 1–16.
   Google Scholar
• D.I. Gallardo, E. Gómez-Déniz, J. Leão, and H.W. Gómez, Estimation and diagnostic tools in reparameterized slashed Rayleigh regression model. An application to chemical data, Chemomet. Intell. Laboratory Syst. 207 (2020), pp. 1–11.
   Web of Science ®Google Scholar
• A.M. Garay, V.H. Lachos, F.V. Labra, and E.M.M. Ortega, Statistical diagnostics for nonlinear regression models based on scale mixtures of skew-normal distributions, J. Statist. Comput. Simul. 84 (2014), pp. 1761–1778.
   Web of Science ®Google Scholar
• V.J. García, E. Gómez-Déniz, and F.J. Vázquez-Polo, A new skew generalization of the normal distribution: properties and applications, Comput. Statist. Data Anal. 54 (2010), pp. 2021–2034.
   Web of Science ®Google Scholar
• R.A. Gordon, Regression Analysis for the Social Sciences, Taylor & Francis, New York, 2015.
   Google Scholar
• G. Haas, L. Bain, and C. Antle, Inferences for the Cauchy distribution based on maximum likelihood estimators, Biometrika 57 (1970), pp. 403–408.
   Web of Science ®Google Scholar
• J. Harezlak, D. Ruppert, and M.P. Wand, Semiparametric Regression with R, Springer, New York, 2018.
   Google Scholar
• D.R. Hunter and K. Lange, Quantile regression via an MM algorithm, J. Comput. Graphical Statist. 9 (2000), pp. 60–77.
   Web of Science ®Google Scholar
• P. Jodrá and M.D. Jiménez-Gamero, A quantile regression model for bounded responses based on the exponential-geometric distribution, REVSTAT-Statistical J. 18 (2020), pp. 415–436.
   Web of Science ®Google Scholar
• R. Koenker and Jr. Bassett, Regression quantiles, Econometrica 46 (1978), pp. 33–50.
   Web of Science ®Google Scholar
• R. Koenker, V. Chernozhukov, X. He, and L. Peng, Handbook of Quantile Regression, CRC Press, Boca Raton, 2017.
   Google Scholar
• J. Leão, V. Leiva, H. Saulo, and V. Tomazella, Birnbaum-Saunders frailty regression models: diagnostics and application to medical data, Biometrical J. 59 (2017), pp. 291–314.
   PubMed Web of Science ®Google Scholar
• A.W. Marshall and I. Olkin, A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families, Biometrika 84 (1997), pp. 641–652.
   Web of Science ®Google Scholar
• J. Mazucheli, A.F.B. Menezes, L.B. Fernandes, R.P. de Oliveira, and M.E. Ghitany, The unit-Weibull distribution as an alternative to the Kumaraswamy distribution for the modeling of quantiles conditional on covariates, J. Appl. Statist. 47 (2020), pp. 954–974.
   PubMed Web of Science ®Google Scholar
• NHLBI, Assessing your weight and health risk, 2022. https://www.nhlbi.nih.gov/health/educational/lose_wt/risk.htm.
   Google Scholar
• NHLBI, Classification of overweight and obesity by BMI, waist circumference, and associated disease risks, 2022. https://www.nhlbi.nih.gov/health/educational/lose_wt/BMI/bmi_dis.htm.
   Google Scholar
• R Core Team, R: a language and environment for statistical computing. R foundation for statistical computing, Vienna, Austria, 2021. https://www.R-project.org/.
   Google Scholar
• R.A. Rigby and D.M. Stasinopoulos, A semi-parametric additive model for variance heterogeneity, Statist. Comput. 6 (1996), pp. 57–65.
   Web of Science ®Google Scholar
• F.J. Rubio and M.F.J. Steel, On the Marshall-Olkin transformation as a skewing mechanism, Comput. Statist. Data Anal. 56 (2012), pp. 2251–2257.
   Web of Science ®Google Scholar
• L. Sánchez, V. Leiva, M. Galea, and H. Saulo, Birnbaum-Saunders quantile regression and its diagnostics with application to economic data, Appl. Stochastic Models Bus. Industry 37 (2021), pp. 53–73.
   Web of Science ®Google Scholar
• G. Schwarz, Estimating the dimension of a model, Ann. Statist. 6 (1978), pp. 461–464.
   Web of Science ®Google Scholar
• M. Sharafi and J. Behboodian, The Balakrishnan skew–normal density, Statist. Papers. 49 (2008), pp. 769–778.
   Web of Science ®Google Scholar
• D. Stasinopoulos and R. Rigby, Generalized additive models for location scale and shape (GAMLSS) in R, J. Statist. Softw. 23 (2008), pp. 1–64.
   Web of Science ®Google Scholar
• M.D. Stasinopoulos, R.A. Rigby, G.Z. Heller, V. Voudouris, and F. De Bastiani, Flexible Regression and Smoothing: Using GAMLSS in R, Chapman & Hall, Boca Raton, 2017.
   Google Scholar
• T.M. Therneau, P.M. Grambsch, and T.R. Fleming, Martingale-based residuals for survival models, Biometrika 77 (1990), pp. 147–160.
   Web of Science ®Google Scholar