#### Non-nested hypothesis tests

I was reading [1]. I must say that I do not know Bayesian methods to cope with model misspecification, tests with an unknown true model, or tests for non-nested hypotheses except Bayes factor (concerns a lot how to choose priors). Nonetheless, the zeal among economists to test non-nested models might assist astronomers to move forward beyond testing nested hypotheses with F statistic.

Knowing that photons follows Poission distribution, that limited numbers of non nested candidate models (one does have physics to constrain models), that generalized linear model (GLM) could expand regression models discussed in [1] to account Poisson behavior, and that there hasn’t been any collaboration between economists and astronomers, citing some papers from economics journals may help astronomers handle non-nested models and test them (and get parameter estimates and proper error bars).

References—–

[1] MacKinnon, J.G. (1983). Model Specification Tests Against Non-Nested Alternatives, Queens’ Economics Department Working Paper, No. 573

[2] Cox, D.R. (1961). Tests of separate families of hypotheses, Proceedings of the fourth Berkeley symposium on mathematical statistics and probability, 1, pp. 105-123

[3] Cox. D.R. (1962). Further results on tests of separate families of hypotheses, JRSS, B, 24, pp. 406-424

[4] White, H. (1982). Maximum likelihood estimation of misspecified models, Econometrica, 50, pp. 1-25

[5] Nishii, R. (1988). Maximum likelihood principle and model selection when the true model is unspecified, Journal of Multivariate Analysis, 27(2), pp. 392-403

[6] Vuoung, Q.H. (1989). Likelihood ratio test for model selection and non-nested hypotheses, Econometrica, 57(2), pp.307-333

[7] Sin, C. & White, H. (1996) Information criteria for selecting possibly misspecified parametric models, Journal of Econometrics, 71, pp.207-225

The non-nested hypothesis testing problem was evolved from [2]&[3]. [4],[5],[6],&[7] are well cited papers on the topic or experienced my readership. Please, advice me if you have more information regarding non-nested hypothesis tests in astronomy.

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