Gross Non-Normality and the Quality of a Simple Approximation to the P-Value of a Routine Test of Non-Nested Regressions

The distribution of certain test statistics for non-nested regressions can be so grossly non-normal that p-values computed on the assumption of approximate normality cannot be safely used for routine inference. This paper presents results on the quality of a new more accurate yet still user-friendly p-value approximation which embodies an inverse measure of the strength of relationship between regressors of competing models. This easily-computed measure is equivalent to the sum of eigenvalues which have recently been shown to characterize the exact finite-sample distribution of the test statistic

Hypothesis testing of multiple inequalities: the method of constraint chaining

Econometric inequality hypotheses arise in diverse ways. Examples include concavity restrictions on technological and behavioural functions, monotonicity and dominance relations, one-sided constraints on conditional moments in GMM estimation, bounds on parameters which are only partially identified, and orderings of predictive performance measures for competing models. In this paper we set forth four key properties which tests of multiple inequality constraints should ideally satisfy. These are (1) (asymptotic) exactness, (2) (asymptotic)similarity on the boundary, (3) absence of nuisance parameters from the asymptotic null distribution of the test statistic, (4) low computational complexity and boostrapping cost. We observe that the predominant tests currently used in econometrics do not appear to enjoy all these properties simultaneously. We therefore ask the question : Does there exist any nontrivial test which, as a mathematical fact, satisfies the first three properties and, by any reasonable measure, satisfies the fourth ? Remarkably the answer is affirmative. The paper demonstrates this constructively. We introduce a method of test construction called chaining which begins by writing multiple inequalities as a single equality using zero-one indicator functions. We then smooth the indicator functions. The approximate equality thus obtained is the basis of a well-behaved test. This test may be considered as the baseline of a wider class of tests. A full asymptotic theory is provided for the baseline. Simulation results show that the finite-sample performance of the test matches the theory quite well

Statistical tests and related results for identification, rank and latent roots

SIGLEAvailable from British Library Document Supply Centre- DSC:D34938/81 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

Characterization of the exact finite-sample distribution of a routine test statistic for non-nested regressions

This paper obtains a complete characterization of the previously unknown exact finite-sample distribution of a routine statistic for testing a linear regression function against a non-nested alternative. Simple approximations to the exact distribution are investigated.Non-nested regressions Most powerful test Eigenvalues Exact finite-sample distribution Student T and root-F mixture Approximations

Quasi-Akaike and Quasi-Schwarz Criteria for Model Selection: A Surprising Consistency Result

This paper gives a theoretical contribution to the issue of model selection, using a moment condition approach in which estimated moments are treated as data to be explained, and in which model selection is based on a quasi Akaike and a quasi Schwarz criteria

Hypothesis testing of multiple inequalities: the method of constraint chaining

Econometric inequality hypotheses arise in diverse ways. Examples include concavity restrictions on technological and behavioural functions, monotonicity and dominance relations, one-sided constraints on conditional moments in GMM estimation, bounds on parameters which are only partially identified, and orderings of predictive performance measures for competing models. In this paper we set forth four key properties which tests of multiple inequality constraints should ideally satisfy. These are (1) (asymptotic) exactness, (2) (asymptotic)similarity on the boundary, (3) absence of nuisance parameters from the asymptotic null distribution of the test statistic, (4) low computational complexity and boostrapping cost. We observe that the predominant tests currently used in econometrics do not appear to enjoy all these properties simultaneously. We therefore ask the question : Does there exist any nontrivial test which, as a mathematical fact, satisfies the first three properties and, by any reasonable measure, satisfies the fourth ? Remarkably the answer is affirmative. The paper demonstrates this constructively. We introduce a method of test construction called chaining which begins by writing multiple inequalities as a single equality using zero-one indicator functions. We then smooth the indicator functions. The approximate equality thus obtained is the basis of a well-behaved test. This test may be considered as the baseline of a wider class of tests. A full asymptotic theory is provided for the baseline. Simulation results show that the finite-sample performance of the test matches the theory quite well