Point Estimation and Tests of Hypotheses in Small Samples

  • Thomas B. Fomby
  • Stanley R. Johnson
  • R. Carter Hill


The ordinary least squares and generalized least squares results reviewed in Chapter 2 dealt with the efficiency of estimation methods in the classical linear regression model and the generalized least squares model. However, small sample statistical inference based on these estimators requires stronger distributional assumptions on the error terms than those made in the previous chapter. In this chapter the distributional properties of the error terms in the classical linear regression model are assumed but, in addition, the error terms are assumed to be normally distributed. This “revised” model is called the classical normal linear regression model. It permits maximum likelihood estimation of the parameters and the construction of likelihood ratio tests of hypotheses.


Likelihood Function Maximum Likelihood Estimator Minimum Variance Unbiased Estimator Joint Test 
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  1. Chow, G. C. (1960). Tests of equality between subsets of coefficients in two linear regressions. Econometrica, 28, 591–605.CrossRefGoogle Scholar
  2. Dhrymes, P. J. (1974), Econometrics (New York: Springer-Verlag).Google Scholar
  3. Fisher, F. (1970). Tests of equality between sets of coefficients in two linear regressions: an expository note. Econometrica, 38, 361–366.CrossRefGoogle Scholar
  4. Hogg, R. V. and Craig, A. T. (1970). Introduction to Mathematical Statistics, 3rd ed. New York: MacMillan.Google Scholar
  5. Kendall, M. G. and Stuart, A. (1973). The Advanced Theory of Statistics, vol. 2, 3rd ed. New York: Hafner.Google Scholar
  6. Nerlove, M. (1963). Returns to scale in electricity supply. In Measurement in Economics: Studies in Mathematical Economics and Econometrics in Memory of Yehuda Grunfeld. Edited by C. F. Christ, M. Friedman, L. A. Goodman, Z. Griliches, A. C. Harberger, N. Liviatan, J. Mincer, Y. Mundlak, M. Nerlove, D. Patinkin, L. G. Telser, and H. Theil. Stanford: Stanford University Press. Pp. 156–198.Google Scholar
  7. Neyman, J. and Pearson, E. S. (1928). On the use and interpretation of certain test criteria for the purposes of statistical inference. Biometrika, A, 20,175-240 (Part 1), 263–294 (Part II).Google Scholar
  8. Schmidt, P. (1976). Econometrics. New York: Marcel Dekker.Google Scholar
  9. Theil, H. (1971). Principles of Econometrics. New York: Wiley.Google Scholar
  10. Tufte, E. (1978). Political Control of the Economy. Princeton, NJ: Princeton University Press.Google Scholar
  11. Wilks, S. (1962). Mathematical Statistics. New York: Wiley.Google Scholar

Copyright information

© Springer Science+Business Media New York 1984

Authors and Affiliations

  • Thomas B. Fomby
    • 1
  • Stanley R. Johnson
    • 2
  • R. Carter Hill
    • 3
  1. 1.Department of EconomicsSouthern Methodist UniversityDallasUSA
  2. 2.The Center for Agricultural and Rural DevelopmentIowa State UniversityAmesUSA
  3. 3.Department of EconomicsLouisiana State UniversityBaton RougeUSA

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