论文信息 - The Likelihood Ratio, Wald, and Lagrange Multiplier Tests: An Expository Note

The Likelihood Ratio, Wald, and Lagrange Multiplier Tests: An Expository Note

Abstract By means of simple diagrams this note gives an intuitive account of the likelihood ratio, the Lagrange multiplier, and Wald test procedures. It is also demonstrated that if the log-likelihood function is quadratic then the three test statistics are numerically identical and have χ2 distributions for all sample sizes under the null hypothesis.

A. Buse

[1] Calyampudi R. Rao. Large sample tests of statistical hypotheses concerning several parameters with applications to problems of estimation , 1948, Mathematical Proceedings of the Cambridge Philosophical Society.

[2] J. Aitchison,et al. Maximum-Likelihood Estimation of Parameters Subject to Restraints , 1958 .

[3] H. Theil. Principles of econometrics , 1971 .

[4] Jan Kmenta,et al. Elements of econometrics , 1988 .

[5] Ernst R. Berndt,et al. CONFLICT AMONG CRITERIA FOR TESTING HYPOTHESES IN THE MULTIVARIATE LINEAR REGRESSION MODEL , 1977 .

[6] B. Efron,et al. Assessing the accuracy of the maximum likelihood estimator: Observed versus expected Fisher information , 1978 .

[7] T. Breurch,et al. A simple test for heteroscedasticity and random coefficient variation (econometrica vol 47 , 1979 .

[8] Trevor Breusch,et al. Conflict among Criteria for Testing Hypotheses: Extensions and Comments , 1979 .

[9] Adrian Pagan,et al. The Lagrange Multiplier Test and its Applications to Model Specification in Econometrics , 1980 .

[10] Michael McAleer,et al. Principles and Methods in the Testing of Alternative Models , 1980 .

[11] A. Buse. Pooling Time Series and Cross Section Data: A Minimum Chi-Squared Approach , 1981 .

[12] N. Savin,et al. Conflict among the Criteria Revisited: The W, LR and LM Tests , 1982 .