Truncated location-scale non linear regression models

References

• A’Hearn, A. (2004). A restricted maximum likelihood estimator for truncated height samples. Econ. Hum. Biol. 2:5–19.
   PubMedGoogle Scholar
• Amemiya, T. (1985). Advanced Econometrics. Cambridge, MA: Harvard University Press.
   Google Scholar
• Arellano-Valle, R.B., Azzalini, A. (2008). The centred parametrization for the multivariate skew-normal distribution. J. Multivariate Anal. 99:1362–1382.
   Web of Science ®Google Scholar
• Azzalini, A. (1985). A class of distributions which includes the normal ones. Scand. J. Stat. 12(2):171–178.
   Web of Science ®Google Scholar
• Azzalini, A., Capitanio, A. (1999). Statistical applications of the multivariate skew normal distribution. J. R. Stat. Soc. Ser. B (Methodological) 61(3):579–602.
   Google Scholar
• Beale, E.M.L. (1960). Confidence regions in non-linear estimation. J. R. Stat. Soc. Series B (Methodological) 22(1):41–88.
   Google Scholar
• Bragato, P.L. (2004). Regression analysis with truncated samples and its application to ground-motion attenuation studies. Bull. Seismol. Soc. Am. 94(4):1369–1378.
   Web of Science ®Google Scholar
• Burdine, N.T. (1953). Relative permeability calculations from pore size distribution data. J. Petrol. Technol. 5(3):71–78.
   Google Scholar
• Chen, S., Zhou, X. (2012). Semiparametric estimation of a truncated regression model. J. Econ. 167:297–304.
   Web of Science ®Google Scholar
• Cohen, A.C. (1991). Truncated and Censored Samples: Theory and Applications. New York: Marcel Dekker.
   Google Scholar
• Conover, W.J., Johnson, M.E., Johnson, M.M. (1981). A comparative study of tests for homogeneity of variances, with applications to the outer continental shelf bidding data. Technometrics 23(4):351–361.
   Web of Science ®Google Scholar
• Cook, R.D. (1977). Detection of influential observations in linear regression. Technometrics 19(1):15–18.
   Web of Science ®Google Scholar
• Cook, R.D., Weisberg, S. (1982). Residuals and Influence in Regression. New York: Chapman & Hall.
   Google Scholar
• Cosslett, S. (2004). Efficient semiparametric estimation of censored and truncated regressions via smoothed self-consistency equation. Econometrica 72:1277–1293.
   Web of Science ®Google Scholar
• Cox, D.R., Hinkley, D.V. (1974). Theoretical Statistics. London: Chapman & Hall.
   Google Scholar
• de Uña Álvarez, J., Liang, H.-Y., Rodríguez-Casal, A. (2010). Nonlinear wavelet estimator of the regression function under left-truncated dependent data. J. Nonparametric Stat. 22(3):319–344.
   Web of Science ®Google Scholar
• Dempster, A.P., Laird, N.M., Rubin, D.B. (1977). Maximum likelihood from incomplete data via the em algorithm. J. R. Stat. Soc. Ser. B 39(1):1–38.
   Google Scholar
• Faires, J.D., Burden, R. (2002). Numerical Methods, 3rd edition. Boston: Brooks Cole.
   Google Scholar
• Ferrari, S.L.P., Cribari-Neto, F. (2004). Beta regression for modelling rates and proportions. J. Appl. Stat. 31(7):799–815.
   Web of Science ®Google Scholar
• Flecher, C., Allard, D., Naveau, P. (2010). Truncated skew-normal distributions: Moments, estimation by weighted moments and application to climatic data. Int. J. Stat. LXVIII(3):331–345.
   Google Scholar
• Fletcher, R. (1987). Practical Methods of Optimization, 2nd edition. Chichester: John Wiley.
   Google Scholar
• Fredlund, D.G., Xing, A. (1994). Equations for the soil-water characteristic curve. Can. Geotech. J. 31(3):521–532.
   Web of Science ®Google Scholar
• Gardner, W.R. (1958). Some steady state solutions of unsaturated moisture flow equations with application to evaporation from water table. Soil Sci. 85:228–232.
   Google Scholar
• Geyer, C.J. (2009). Trust: trust region optimization. R package version 0.1-2.
   Google Scholar
• Gilbert, P., Varadhan, R. (2012). numDeriv: Accurate Numerical Derivatives. R package version 2012.9-1.
   Google Scholar
• Hausman, J.A., Wise, D.A. (1977). Social experimentation, truncated distributions, and efficient estimation. Econometrica 45(4):919–938.
   Web of Science ®Google Scholar
• Heckman, J.J. (1976). The common structure of statistical models of truncation, sample selection and limited dependent variables and a simple estimator for such models. Ann. Econ. Social Meas. 5(4):475–492.
   Google Scholar
• Hudson, D.J. (1971). Interval estimation from the likelihood function. J. R. Stat. Soc. Series B (Methodological) 33(2):256–262.
   Google Scholar
• Jamalizadeh, A., Pourmousa, R., Balakrishnan, N. (2009). Truncated and limited skew-normal and skew-t distributions: Properties and an illustration. Commun. Stat. Theory Methods 38:2653–2668.
   Web of Science ®Google Scholar
• Johnson, N.L., Kotz, S., Balakrishnan, N. (1994). Continuous Univariate Distributions, Volume 1, 2nd edition. New York: Wiley.
   Google Scholar
• Klein, J.P., Moeschberger, M.L. (2003). Survival Analysis: Techniques for Censored and Truncated Data, 2nd edition. Statistics for Biology and Health. New York: Springer-Verlag.
   Google Scholar
• Lee, L.F. (1992). Semiparametric nonlinear least-square estimation of truncated regression models. Econ. Theory 8:52–94.
   Web of Science ®Google Scholar
• Lee, M. (1993). Quadratic mode regression. J. Econ. 57:1–19.
   Web of Science ®Google Scholar
• Lehmann, E.L., Casella, G. (1998). Theory of Point Estimation, 2nd edition. New York: Springer.
   Google Scholar
• Leong, E.C., Rahardjo, H. (1997). Review of soil water characteristic curve equations. J. Geotech. Geoenviron. Eng. 123(12):1106–1117.
   Web of Science ®Google Scholar
• Levene, H. (1960). In Contributions to Probability and Statistics: Essays in Honor of Harold Hotelling (pp. 278–292). California: Stanford University Press.
   Google Scholar
• Lindsey, J.K., Altham, P.M.E. (1998). Analysis of the human sex ratio by using overdispersion models. J. R. Stat. Soc. Series C (Applied Statistics) 47(1):149–157.
   PubMed Web of Science ®Google Scholar
• Luebeck, G., Meza, R. (2013). Bhat: General likelihood exploration. R package version 0.9-10.
   Google Scholar
• Maddala, G.S. (1983). Limited Dependent and Qualitative Variables in Econometrics. New York: Cambridge.
   Google Scholar
• Martinez, E.H., Varela, H., Gomez, H.W., Bolfarine, H. (2006). A note on the likelihood and moments of the skew-normal distribution. SORT 32(1):57–66.
   Web of Science ®Google Scholar
• Meng, X.L., Rubin, D.B. (1993). Maximum likelihood estimation via the ecm algorithm: A general framework. Biometrika 80(2):267–278.
   Web of Science ®Google Scholar
• Monti, A.C. (2003). A note on the estimation of the skew normal and the skew exponential power distributions. METRON - Int. J. Stat. LXI(2):205–219.
   Google Scholar
• Mualem, Y. (1976). A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resour. Res. 12:593–622.
   Web of Science ®Google Scholar
• Nadarajah, S., Kotz, S. (2008). Moments of truncated t and f distributions. Portuguese Econ. J. 7(1):63–73.
   Web of Science ®Google Scholar
• Nelson, C.H., Preckel, P.V. (1989). The conditional beta distribution as a stochastic production function. Am. J. Agric. Econ. 71(2):370–378.
   Web of Science ®Google Scholar
• Newey, W. (2004). Efficient semiparametric estimation via moment restrictions. Econometrica 72:1877–1897.
   Web of Science ®Google Scholar
• Ould-Saïd, E., Lemdani, M. (2006). Asymptotic properties of a nonparametric regression function estimator with randomly truncated data. Ann. Inst. Stat. Math. 85(2):357–378.
   Web of Science ®Google Scholar
• Pawitan, Y. (2001). In All Likelihood: Statistical Modelling and Inference Using Likelihood. New York: Oxford University Press.
   Google Scholar
• Pewsey, A. (2000). Problems of inference for Azzalini’s skew normal distribution. J. Appl. Stat. 27(7):859–870.
   Web of Science ®Google Scholar
• Piessens, R., deDoncker Kapenga, E., Uberhuber, C., Kahaner, D. (1983). Quadpack: A Subroutine Package for Automatic Integration. Berlin: Springer Verlag.
   Google Scholar
• Powell, J. (1986). Symmetrically trimmed least squares estimation for tobit models. Econometrica 54:1435–1460.
   Web of Science ®Google Scholar
• R Core Team. (2013). R: a language and environment for statistical computing. R Foundation for Statistical Computing. ISBN 3-900051-07-0.
   Google Scholar
• Richardson, L.F. (1911). The approximate arithmetical solution by finite differences of physical problems including differential equations, with an application to the stresses in a masonry dam. Philos. Trans. R. Soc. London, Ser. A 210(459–470):307–357.
   Google Scholar
• Richardson, L.F., Gaunt, J.A. (1927). The deferred approach to the limit. Philos. Trans. Royal Soc. London, Ser. A 226(636–646):307–357.
   Google Scholar
• Rodrigues, L.N., Maia, A.H.N. (2011). Funções de pedotransferência para estimar a condutividade hidráulica saturada e as umidades de saturação e residual do solo em uma bacia hidrográfica do cerrado. In XIX Simpósio brasileiro de recursos hídricos.
   Google Scholar
• Sartori, N. (2006). Bias prevention of maximum likelihood estimates for scalar skew normal and skew t distributions. J. Stat. Plann. Inference 136(12):4259–4275.
   Web of Science ®Google Scholar
• Sillers, W.S., Fredlund, D.G., Zakerzadeh, N. (2001). Mathematical attributes of soil-water characteristic curves models. Geotech. Geol. Eng. 19:243–283.
   Google Scholar
• van Genuchten, M.T. (1980). A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44:892–898.
   Web of Science ®Google Scholar
• Venzon, D.J., Moolgavkar, S.H. (1988). A method for computing profile-likelihood based confidence intervals. J. R. Stat. Soc. Ser. C (Appl. Stat.) 37(1):87–94.
   Web of Science ®Google Scholar
• White, H. (1980). A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica 48(4):817–838.
   Web of Science ®Google Scholar
• Wolfram Research, Inc. (2010). Mathematica. version 8.0. Champaign, IL.
   Google Scholar