Abstract: In the recent years there is a large application of large sample tests in many scientific investigations. The commonly used large sample tests are Likelihood ratio tests, Wald and Score tests. Wald and Score tests make use of expected fisher information in computation of test statistic. In complex problems the expressions for fisher information cannot be derived and it is customary to use the observed fisher information in place of the expected fisher information for these tests. The unanswered questions are 1) What happens to the size and power of Wald and Score test if we use observed fisher information .2) What happens if fisher information is evaluated at restricted MLE of parameter for Wald test? 3) What is the implication of fisher information evaluated at unrestricted MLE for Score test?
This paper makes an attempt to answer these questions. Extensive simulations have been carried out to answer these questions in testing for location parameter θ of Cauchy distribution and testing for parameter λ of zero Inflated Poisson distribution. The results indicate that the test statistic using observed fisher information maintain power and size when compared to the test statistic using expected fisher information. Further if the parameter under consideration is univariate then it is suggested to use Wald test with observed fisher information evaluated at restricted MLE of θ. If the parameter under consideration is bivariate then our investigation suggests Score test with observed fisher information using restricted MLE of λ.
Key Words: Large sample tests, Wald tests .Score tests, Expected fisher information, Observed fisher information restricted and unrestricted MLE
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