Introduction
The Neyman–Pearson theory of hypothesis testing applies if the models belong to the same family of distributions. Alternatively, special procedures are needed if the models belong to families that are separate or non-nested, in the sense that an arbitrary member of one family cannot be obtained as a limit of members of the other.
Let y = (y 1, …, y n ) be independent observations from some unknown distribution. Suppose that there are null and alternative hypotheses H f and H g specifying parametric densities f(y, α) and g(y, β) for the random vector y. Hence α and β are unknown vector parameters and it is assumed that the families are separate.
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References and Further Reading
Araújo MI, Pereira BB (2007) Comparison among Bayes factors for separate models: some simulation results. Commun Stat – Simul Comput 36:297–309
Araújo MI, Fernandes M, de B Pereira B (2005) Alternative procedures to discriminate non nested multivariate linear regression models. Commun Stat – Theory Methods 34:2047–2062
Atkinson AC, Cox DR (1974) Planning experiments for discriminating between models (with discussion). J R Stat Soc B 36:321–348
Chambers EA, Cox DR (1967) Discriminating between alternative binary response models. Biometrica 54:573–578
Cox DR (1961) Tests of separate families of hypotheses. In: Proceedings of fourth Berkeley symposium, vol 1, pp 105–123
Cox DR (1962) Further results on tests of separate families of hypotheses. J R Stat Soc B 24:406–423
Cox DR (1974) Discussion of “Dempster, A.P. pg 353 – The direct use of likelihood for significance testing”. In: Proceedings of conference on foundational questions in statistical inference, Aarhus. Memoirs no. 1. University of Aarhus, Aarhus
Cox DR, Brandwood L (1959) On a discriminatory problem connected with the works of Plato. J R Stat Soc B 21:195–200
Davidson R, MacKinnon JD (1983) Testing the specification of multivariate models in the presence of alternative hypotheses. J Econom 23:301–313
de B Pereira B (1977a) A note on the consistency and on finite sample comparisons of some tests of separate families of hypotheses. Biometrika 64:109–113 (correction in volume 64, page 655)
de B Pereira B (1977b) Discriminating among separate models: a bibliography. Int Stat Rev 45:163–172
de B Pereira B (1978) Empirical comparisons of some tests of separate families of hypotheses. Metrika 25:219–234
de B Pereira B (1981) Discriminating among separate models: an additionalbibliography. Int Stat Inf 62(2):3 (repr Katti SK (1982) On the preliminary test for the CEAS model versus the Thompson model for predicting soybean production. Technical Report 125, Department of Statistics, University of Missouri – Columbia)
de B Pereira B (1998) Separate families of hypotheses. In: Armitage P, Colton T (eds) Encyclopedia of biostatistics, vol 5. Wiley, pp 4069–4074
de B Pereira B (2005) Separate families of hypotheses. In: Armitage P, Colton T (eds) Encyclopedia of biostatistics, vol 7, 2nd edn. Wiley, pp 4881–4886
Gourieroux C, Monfort A (1994) Testing non-nested hypotheses. In: Engle R, McFadden DL (eds) Handbook of econometrics, vol IV (Chapter 44). Elsevier, London, pp 2585–2637
McAller M (1995) The significance of testing empirical non-nested models. J Econom 65:149–171
McAller M, Pesaran MH, Bera AK (1990) Alternative approaches to testing non-nested models with autocorrelated disturbances. Commun Stat – Theory Methods 19:3619–3644
Pesaran MH (1982) On the comprehensive method for testing non-nested regression models. J Econom 18:263–274
Pesaran MH, Deaton AS (1978) Testing non-nested regression models. Econometrica 46:677–694
Pesaran MH, Weeks M (2001) Non-nested hypothesis testing: an overview. In: Baltagi BH (ed) Companion to theoretical econometrics. Basil Blackwell, Oxford
Timm NH, Al-Subaihi AA (2001) Testing model specification in seemingly unrelated regression models. Commun Stat – Theory Methods 30:577–590
Uloa RD, Pesaran MH (2008) Non-nested hypotheses. In: Durlauf SN, Blume LE (eds) The new Palgrave dictionary of economics, 2nd edn. Palgrave Macmillan
Vuong QH (1989) Likelihood ratio tests for model selection and non-nested hypothesis. Econometrica 57:307–333
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de Pereira, B.B. (2011). Tests for Discriminating Separate or Non-Nested Models. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_589
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