Simple techniques for the graphical display of simulation evidence concerning the size and power of hypothesis tests are developed and illustrated. Three types of figures - called P value plots, P value discrepancy plots, and size-power curves - are discussed. Some Monte Carlo experiments on the...

We develop a new form of the information matrix test for a wide variety of statistical models, and present full details for the special case of univariate nonlinear regression models. Chesher (1984) showed that the implicit alternative of the information matrix test is a model with random...

We consider several issues related to what Hausman (1978) called "specification tests", namely tests designed to verify the consistency of parameter estimates. We first review a number of results about these tests in linear regression models, and present some new material on their distribution...

In a recent paper, Plosser, Schwert and White (1982) proposed a general test for model misspecification based on a comparison of estimates of the model in levels and first-differences. We demonstrate that this test is equivalent to a certain F test for omitted variables. The latter test has...

The local power of test statistics is analyzed by extending the notion of Pitman sequences to sequences of data-generating processes (DGPs) that approach the null hypothesis without necessarily satisfying the alternative hypothesis. Under quite general conditions, the three classical test...

Methods based on linear regression provide a very easy way to use the information in control and antithetic variates to improve the efficiency with which certain features of the distributions of estimators and test statistics are estimated in Monte Carlo experiments. We propose a new technique...

We develop simple procedures to test for omitted variables and perform other tests in regression directions, which are asymptotically valid in the presence of heteroskedasticity of unknown form. We examine the asymptotic behaviour of these tests, and use Edgeworth approximations to study their...

Associated with every popular nonlinear estimation method is at least one "artificial" linear regression. We define an artificial regression in terms of three conditions that it must satisfy. Then we show how artificial regressions can be useful for numerical optimization, testing hypotheses,...

In practice, bootstrap tests must use a finite number of bootstrap samples. This means that the outcome of the test will depend on the sequence of random numbers used to generate the bootstrap samples, and it necessarily results in some loss of power. We examine the extent of this power loss and...