Large Sample Point Estimation and Tests of Hypotheses
In the last chapter it was shown that certain properties of estimators and test statistics hold for any given sample size T provided appropriate assumptions are satisfied. In general, the extent of the conclusions depends upon the extent of the assumptions; best linear unbiased was provided with the assumption of independent and identically distributed errors while the additional assumption of normality of the errors lead to minimum variance unbiased efficiency and the elimination of the linearity requirement. Unfortunately, such strong results as minimum variance unbiased efficiency are not always obtainable in econometric modeling. For example, in feasible generalized least squares, lagged dependent variable models, and simultaneous equations, the derivation of small sample properties of estimators is not generally possible. Instead, the evaluation of these estimators must be based on their behavior in samples of infinite size. The idea of large sample efficiency involves new concepts yet to be discussed.
KeywordsCumulative Distribution Function Maximum Likelihood Estimator Asymptotic Distribution Consistent Estimator Asymptotic Variance
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- Cramér, H. (1946). Mathematical Methods of Statistics. Princeton, NJ: Princeton University Press.Google Scholar
- Dhrymes, P. J. (1974). Econometrics. New York: Springer-Verlag.Google Scholar
- Gnedenko, B. (1962). The Theory of Probability. New York: Chelsea.Google Scholar
- Kendall, M. G. and Stuart, A. (1973). The Advanced Theory of Statistics, vol. 2, 3rd ed. New York: Hafner.Google Scholar
- Schmidt, P. (1976). Econometrics. New York: Marcel Dekker.Google Scholar
- Theil, H. (1971). Principles of Econometrics. New York: Wiley.Google Scholar
- Wilks, S. (1962). Mathematical Statistics. New York: Wiley.Google Scholar