Tests Of Non-nested Regression Models Research Articles

A simple test for regression specification with non-nested alternatives

In this paper, I introduce a simple test for the presence of the data-generating process among several non-nested alternatives. The test is an extension of the classical J test for non-nested regression models. I also provide a bootstrap version of the test that avoids possible size distortions inherited from the J test.

Bootstrap J tests of nonnested linear regression models

The J test for nonnested regression models often overrejects very severely as an asymptotic test. We provide a theoretical analysis which explains why and when it performs badly. This analysis implies that, except in certain extreme cases, the J test will perform very well when bootstrapped. Using several methods to speed up the simulations, we obtain extremely accurate Monte Carlo results on the finite-sample performance of the bootstrapped J test. These results fully support the predictions of our theoretical analysis, even in contexts where the analysis is not strictly applicable.

Tests of non-nested regression models some results on small sample behaviour and the bootstrap

The most popular procedures for testing a regression model against a single non-nested alternative can be substantially oversized in small samples. Also, when a regression model is to be tested in the presence of several non-nested alternatives, the null model is sometimes accepted only if testing against each alternative in turn produces no significant outcomes. This approach leads to an implicit overall test with a significance level that is not known, even asymptotically. It is shown that the bootstrap can be used to control significance levels in both types of situation. Power estimates for various tests using bootstrap critical values are also obtained and compared.

Semiparametric Specification Testing of Non-nested Econometric Models

We propose a specification test of a parametrically specified nonlinear model against a weakly specified non-nested alternative. We estimate the alternative model by using nonparametric regression (nearest neighbours). The test is based on the t-statistic of an artificial regression. MonteCarlo simulations suggest that the test has good power and size characteristics. In this paper we propose a specification test for non-nested regression models where the alternative hypothesis is nonparametric. Therefore, the regressors in the null and in the alternative are non-nested. The proposed test is based on an artificial nesting procedure in the spirit of the Davidson and MacKinnon (1981) tests. We provide a natural extension of their results in a semiparametric environment. The performance of the alternative under 'the truth of the null' forms the basis for a test of the latter. We use k-nearest neighbour (k-NN) regression to estimate that a possible misspecified parameterization will have on testing the validity of the null. The consistency of the proposed test statistic, under fixed alternatives, is derived under the type of regulatory conditions required when the alternative model is parametrically specified. Nonparametric functional estimation has been recently used in deriving various specification tests. Specification tests of nonparametric and semiparametric restrictions based on average derivatives of the regression function have been considered by Stoker (1989) and Robinson (1989). Cox et al. (1988) considered generalized spline models for testing a parametric null hypothesis against semiparametric alternatives. Eubank and Spiegelman (1990) proposed a spline based method for testing the goodness of fit of a linear model. Wooldridge (1992) derived a residual based test which allows for certain non-fixed nonparametric alternatives. A Davidson and MacKinnon (1981)type test is shown to be consistent using a sieve estimator for the alternatives. In the next section we discuss the proposed test. In Section 3 we investigate the small sample properties of our test by means of a small Monte Carlo. Finally we conclude. The proofs are in the Appendix.

Tests of non-nested regression models

Abstract It is known that the small sample significance levels of Cox-type tests of non-nested regression models can be much greater than the nominal level. Adjustments designed to overcome this problem are discussed and two tests are proposed. Monte Carlo evidence on the performance of the tests derived in this paper, the Davidson-MacKinnon J -test and the Fisher-McAleer test is presented. The F -test applied to the comprehensive model is also included in the simulation experiments.

Comparison of Local Power of Alternative Tests of Non-Nested Regression Models

The paper derives and compares the local power of three different methods of testing non-nested regression models that are available in the literature. It shows that the asymptotic power of the orthodox F test against local alternatives is strictly less than that of Cox's non-nested test or the J test recently proposed by Davidson and MacKinnon [5], unless the number of non-overlapping variables of the alternative hypothesis over the null hypothesis is unity, in which case all three tests are shown to be asymptotically equivalent. The final section of the paper gives results of Monte Carlo experiments designed to check the validity of the theoretical findings of the paper and also to shed light on the small sample properties of the Cox test and the orthodox test.

On the comprehensive method of testing non-nested regression models

The paper derives the specific form of the exponentially combined likelihood function of two competing multivariate non-linear regression models and shows that the application of the comprehensive approach to testing non-nested regression models will, in general, be indeterminate. It establishes that in the univariate case there exists a large number of tests of non-nested regression models which are consistent in addition to having the same asymptotic distribution under the null hypothesis. The paper then derives a set of conditions under which all these consistent tests are asymptotically equivalent not only under the null hypothesis but also under local alternatives. As an application of this latter result the paper establishes the asymptotic equivalence of the tests recently proposed by Davidson and MacKinnon, and Fisher and McAleer under local alternatives, and shows that within the class of tests considered in the paper these proposed tests possess maximum local power. The latter test has this property only when the number of explanatory variables of the ‘true’ model is not more than that of the ‘false’ model.

A small sample test for non-nested regression models

Abstract In this note it is demonstrated that a test for non-nested regression models proposed by Fisher and McAleer (1981) has the Student's t-distribution in small samples. It is also demonstrated that the large sample test of Davidson and MacKinnon (1980, 1981) favours the more parsimonious model specification as compared with the test of Fisher and McAleer.