Non-nested hypothesis testing inference for GAMLSS models

References

• Pearson K. Mathematical contributions to the theory of evolution. III. regression, heredity and panmixia. Philos Trans R Soc Lond. 1896;187:253–318. doi:10.1098/rsta.1896.0007
   Google Scholar
• Nelder JMK, Wedderburn R. Generalized linear models. J Roy Statist Soc A. 1972;135:370–384. doi:10.2307/2344614
   Web of Science ®Google Scholar
• Hastie TJ, Tibshirani RJ. Generalized additive models. Statist Sci. 1986;1:297–318. doi:10.1214/ss/1177013604
   Google Scholar
• Hastie TJ, Tibshirani RJ. Generalized additive models. London (UK): Chapman and Hall; 1990.
   Google Scholar
• Ferrari SLP, Cribari-Neto F. Beta regression for modelling rates and proportions. J Appl Stat. 2004;31:799–815. doi:10.1080/0266476042000214501
   Web of Science ®Google Scholar
• Rigby RA, Stasinopoulos DM. The GAMLSS project: a flexible approach to statistical modelling. In: Klein B, Korsholm L, editors. New trends in statistical modelling: proceedings of the 16th international workshop on statistical modelling. Odense: Denmark; 2001. p. 337–345.
   Google Scholar
• Rigby RA, Stasinopoulos DM. Generalized additive models for location, scale and shape (with discussion). Appl Stat. 2005;54:507–554.
   Web of Science ®Google Scholar
• Akantziliotou K, Rigby RA, Stasinopoulos DM. The R implementation of generalized additive models for location, scale and shape. In: Stasinopoulos M, Touloumi G, editors. Statistical modelling in society: proceedings of the 17th international workshop on statistical modelling. Greece: Chania; 2002. p. 75–83.
   Google Scholar
• Cribari-Neto F, Lucena SEF. Nonnested hypothesis testing in the class of varying dispersion beta regressions. J Appl Stat. 2015;42:967–985. doi:10.1080/02664763.2014.993368
   Web of Science ®Google Scholar
• Cox D. Tests of separated families of hypothesis. Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability. 1961;1:105–123.
   Google Scholar
• Cox D. Further results on tests of separate families of hypotheses. J R Stat Soc B. 1962;24:406–424.
   Google Scholar
• Cox DR. A return to an old paper: tests of separate families of hypotheses. J R Stat Soc B. 2013;75:207–215. doi:10.1111/rssb.12003
   Google Scholar
• Pesaran MH, Weeks M. Non-nested hypothesis testing: an overview. In: Baltagi BH, editor. A companion to theoretical econometrics. Malden (MA): Blackwell; 2001. p. 279–309.
   Google Scholar
• Sayyareh A. Inference after separated hypotheses testing: an empirical investigation for linear models. J Stat Comput Simul. 2012;82:1275–1286. doi:10.1080/00949655.2011.575783
   Web of Science ®Google Scholar
• Atkinson A. A method for discriminating between models (with discussion). J R Stat Soc B. 1970;32:323–353.
   Google Scholar
• Davidson R, MacKinnon J. Several tests for model specification in the presence of alternative hypotheses. Econometrica. 1981;49:781–793. doi:10.2307/1911522
   Web of Science ®Google Scholar
• Deaton AS. Model selection procedures, or, does the consumption function exist? In: Show CG, Corsi P, editors. Evaluating the reliability of macroeconomic models. New York: Wiley; 1982. p. 43–65.
   Google Scholar
• Dastoor N. Some aspects of testing nonnested hypotheses. J Econometrics. 1983;21:213–218. doi:10.1016/0304-4076(83)90014-3
   Web of Science ®Google Scholar
• Gouriéroux C, Monfort A, Trognon A. Testing nested or nonnested hypotheses. J Econometrics. 1983;21:83–115. doi:10.1016/0304-4076(83)90121-5
   Web of Science ®Google Scholar
• Mizon GE, Richard JF. The encompassing principle and its applications to non-nested hypotheses. Econometrica. 1986;54:657–678. doi:10.2307/1911313
   Web of Science ®Google Scholar
• Godfrey LG. Robust non-nested testing for ordinary least squares regression when some of the regressors are lagged dependent variables. Oxf Bull Econ Stat. 2011;73:651–668. doi:10.1111/j.1468-0084.2010.00630.x
   Web of Science ®Google Scholar
• McAleer M. The significance of testing empirical non-nested models. J Econometrics. 1995;67:149–171. doi:10.1016/0304-4076(94)01631-9
   Web of Science ®Google Scholar
• Wooldridge JM. A unified approach to robust, regression-based specification tests. Econometric Theory. 1990;6:17–43. doi:10.1017/S0266466600004898
   Web of Science ®Google Scholar
• Michelis L. The distribution of the J and Cox non-nested tests in regression models with weakly correlated regressors. J Econometrics. 1999;93:369–401. doi:10.1016/S0304-4076(99)00026-3
   Web of Science ®Google Scholar
• Davidson R, MacKinnon JG. Bootstrap J tests of nonnested linear regression models. J Econometrics. 2002;109:167–193. doi:10.1016/S0304-4076(01)00146-4
   Web of Science ®Google Scholar
• Sapra SK. Robust nonnested hypothesis testing. Appl Econ Lett. 2008;15:1–4. doi:10.1080/13504850600605994
   Web of Science ®Google Scholar
• Kelejian HH. A spatial J-test for model specification against a single or a set of non-nested alternatives. LSRS. 2008;1:3–11.
   Google Scholar
• Kelejian HH, Piras G. An extension of the J-test to a spatial panel data framework. J Appl Econometrics. 2014;31:387–402. doi:10.1002/jae.2425
   Web of Science ®Google Scholar
• Burridge P, Fingleton B. Bootstrap inference in spatial econometrics: the J-test. Spat Econ Anal. 2010;5:93–119. doi:10.1080/17421770903511346
   Web of Science ®Google Scholar
• Piras G, Lozano-Garcia N. Spatial J-test: some Monte Carlo evidence. Stat Comput. 2012;22:169–183. doi:10.1007/s11222-010-9215-y
   Web of Science ®Google Scholar
• Ghali M, Krieg JM, Rao KS. A Bayesian extension of the J-test for non-nested hypotheses. J Quant Econ. 2011;9:53–72.
   Google Scholar
• Ramalho EA, Ramalho JJS, Murteira JMR. Alternative estimating and testing empirical strategies for fractional regression models. J Econom Surv. 2011;25:19–68. doi:10.1111/j.1467-6419.2009.00602.x
   Web of Science ®Google Scholar
• Hagemann A. A simple test for regression specification with non-nested alternatives. J Econometrics. 2012;166:247–254. doi:10.1016/j.jeconom.2011.09.037
   Web of Science ®Google Scholar
• Rigby RA, Stasinopoulos DM. Using the Box–Cox t distribution in GAMLSS to model skewness and kurtosis. Stat Model. 2006;6:209–229. doi:10.1191/1471082X06st122oa
   Web of Science ®Google Scholar
• A Language and Environment for Statistical Computing [computer software]. Vienna (Austria): R Foundation for Statistical Computing; 2013.
   Google Scholar
• Stasinopoulos DM, Rigby RA. Generalized additive models for location scale and shape (GAMLSS) in R. J Statist Softw. 2008;23:1–46.
   Web of Science ®Google Scholar
• Rigby B, Stasinopoulos M, Heller G, et al. The distribution toolbox of GAMLSS. London (UK): The GAMLSS Team; 2014.
   Google Scholar
• Cole TJ, Green PJ. Smoothing reference centile curves: the LMS method and penalized likelihood. Stat Med. 1992;11:1305–1319. doi:10.1002/sim.4780111005
   PubMed Web of Science ®Google Scholar
• Rigby R, Stasinopoulos D. A semi-parametric additive model for variance heterogeneity. Statist Comput. 1996;6:57–65. doi:10.1007/BF00161574
   Web of Science ®Google Scholar
• Rigby R, Stasinopoulos M. Mean and dispersion additive models. In: Hardle W, Schimek MG, editors. Statistical theory and computational aspects of smoothing. contributions to statistics. London (UK): Physica-Verlag HD; 1996. p. 215–230.
   Google Scholar
• Nagelkerke NJD. A note on a general definition of the coefficient of determination. Biometrika. 1991;78:691–692. doi:10.1093/biomet/78.3.691
   Web of Science ®Google Scholar
• Crowder MJ, Kimber AC, Smith RL, et al. Statistical analysis of reliability data. London (UK): Chapman and Hall; 1991.
   Google Scholar
• Fan Y, Li Q. Bootstrapping J-type tests for non-nested regression models. Econom Lett. 1995;48:107–112. doi:10.1016/0165-1765(94)00595-S
   Web of Science ®Google Scholar
• Godfrey L. Tests of non-nested regression models: some results on small sample behaviour and the bootstrap. J Econometrics. 1998;84:59–74. doi:10.1016/S0304-4076(97)00079-1
   Web of Science ®Google Scholar
• Smithson M, Verkuilen J. A better lemon squeezer? Maximum likelihood regression with beta-distributed dependent variables. Psychol Methods. 2006;11:54–71. doi:10.1037/1082-989X.11.1.54
   PubMed Web of Science ®Google Scholar
• Ospina R, Ferrari SLP. A general class of zero-or-one inflated regression models. Comput Statist Data Anal. 2012;56:1609–1623. doi:10.1016/j.csda.2011.10.005
   Web of Science ®Google Scholar