Marginal Likelihood-based One-sided LR Test for Testing Higher Order Autocorrelation in Presence of Nuisance Parameters-A Distance Based Approach

Abstract

In most of the cases, only a subvector of the parameters is tested in a model. The remaining parameters arise in the tests as nuisance parameters. The presence of nuisance parameters causes biases in key estimates used in the tests. So inferences made on the presence of nuisance parameters may lead to less accurate conclusions. Even the presence of nuisance parameters can destroy the test. Thus in eliminating the influence of nuisance parameters from the test can improve the tests' performance. The effect of the nuisance parameters can be eliminated by the marginal likelihood, conditional likelihood, canonical likelihood, profile likelihood and Bayesian tests. This paper is concerned with marginal likelihood-based test for eliminating the influence of nuisance parameters. In general, existing one-sided and two-sided tests for autocorrelation are tested only autocorrelation coefficients but not the regression coefficients in the model. So we proposed a distance-based marginal likelihood one-sided Likelihood Ratio (DMLR) test in eliminating the influence of nuisance parameters for testing higher order autocorrelation with one-sided alternatives in linear regression model using marginal likelihood and distance-based approach. Monte Carlo simulations are conducted to compare power properties of the proposed DMLR test with their respective conventional counterparts. It is found that the DMLR test shows substantially improved power for most of cases considered.