Testing for parameter constancy in linear regressions: an empirical distribution function approach

Article Abstract:

Additional tools are proposed for testing parameter instability in linear regressions. Weighted empirical distribution functions of estimated residuals which are asymptotically distribution free were used in the tests. It is demonstrated that the proposed tests could detect changes in regression parameters and changes in variances. The tests could diagnose changes in higher moments or changes in error distribution functions. They are also not very sensitive to deviations from normality.

Testing, Convergence (Mathematics), Distribution (Probability theory)

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Admissibility of the likelihood ratio test when the parameter space is restricted under the alternative

Article Abstract:

Hypothesis tests are studied when the alternative hypothesis restricts the parameter space. Popular examples are multivariate one-sided tests. It is demonstrated that the likelihood ratio test is admissible and maximizes power against other choices which are arbitrarily separated from the null hypothesis. Exact findings are first derived for Gaussian linear regression models with known variance. Asymptotic analogues are developed for dynamic linear models.

Usage, Gaussian processes

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Inference when a nuisance parameter is not identified under the null hypothesis

Article Abstract:

A simulation technique is developed for inference cases where nuisance parameters are not identified under the null hypothesis. The method featured stochastic regression and weak dependence, which were generated in an additive nonlinearity form. The technique yielded a conditional transformation that defined an analogous asymptotic p-value and followed an asymptotic uniform distribution.

Asymptotic distribution (Probability theory)

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