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.
Highlights
IntroductionThe inference in the presence of nuisance parameters (the parameters not under test) is a long-standing problem in econometrics as well as in statistics
The inference in the presence of nuisance parameters is a long-standing problem in econometrics as well as in statistics
This section compares the powers of the existing two-sided LR test, one-sided distance-based one-sided LR (DLR) test and the newly proposed distance-based marginal likelihood one-sided LR (DMLR) tests for testing H1, in the context of linear regression model (2.1), which involves nuisance parameters
Summary
The inference in the presence of nuisance parameters (the parameters not under test) is a long-standing problem in econometrics as well as in statistics. The one-sided and partially one-sided tests may be able to improve the quality of inferences In such situation, the maximum likelihood based LR test can be improved by using distance-based approach for testing higher order autocorrelation in presence of nuisance parameters. Our particular focus in this paper is on the use of maximum likelihood-based LR test (Ara & King, 1993) with distance-based approach (Majumder & King, 1999) for testing higher order autocorrelation in the linear regression model that involves nuisance parameters. Make a comparative study of one-sided maximum likelihoodbased LR test (DMLR) with one-sided LR (DLR) and usual two-sided LR tests for testing higher order autocorrelation in linear regression model that involves nuisance parameters.
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