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Chapter 15
APPROXIMATING THE DISTRIBUTIONS OF
ECONOMETRIC ESTIMATORS AND TEST STATISTICS
THOMAS J. ROTHENBERG*
University of Culijornia, Berkeley
Contents
1. Introduction 882
2. Alternative approximation methods 884
2.1. Preliminaries 884
2.2. Curve-fitting 886
2.3. Transformations 887
2.4. Asymptotic expansions 889
2.5. Ad hoc methods 891
3. Edgeworth approximations 892
3.1. Sums of independent random variables 893
3.2. A general expansion 896
3.3. Non-normal expansions 900
4. Second-order comparisons of estimators 902
4.1. General approach 903
4.2. Optimality criteria 904
4.3. Second-order efficient estimators 905
4.4. Deficiency 907
4.5. Generalizations 908
5. Second-order comparisons of tests 909
5.1. General approach 909
5.2. Some results when 4 = 1 912
5.3. Results for the multiparameter case 915
5.4. Confidence intervals 917
6. Some examples 918
6.1. Simultaneous equations 918
6.2. Autoregressive models 925
6.3. Generalized least squares 929
6.4. Departures from normality 930
7. Conclusions 931
References 932
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