Hostname: page-component-8448b6f56d-jr42d Total loading time: 0 Render date: 2024-04-23T16:58:30.043Z Has data issue: false hasContentIssue false
  • English
  • Français

Interpretation of Graphs that Compare the Distribution Functions of Estimators

Published online by Cambridge University Press:  11 February 2009

Brent R. Moulton
Brent R. Moulton
Affiliation:
U.S. Bureau of Labor Statistics
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper I examine graphical comparisons of one-dimensional (or marginal) distribution functions of alternative estimators. It is shown that areas under the c.d.f. (cumulative distribution function) curve can be given a decision-theoretic interpretation as risk under a bounded absolute-error loss function. I also show that by a simple rescaling of the graph's axes, graphical areas are created which can be interpreted as risk under bounded squared-error loss. The bounded loss functions are applied to compare graphically and numerically the risk of exact distributions of the limited-information maximum likelihood and two-stage least-squares estimators in a simultaneous equations model.

Type
Articles
Information
Econometric Theory , Volume 6 , Issue 1 , March 1990 , pp. 97 - 102
Copyright
Copyright © Cambridge University Press 1990

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Anderson, T. W.An asymptotic expansion of the distribution of the limited information maximum likelihood estimate of a coefficient in a simultaneous equation system. Journal of the American Statistical Association 69 (1974): 565–573.CrossRefGoogle Scholar
2.Anderson, T.W. Some recent developments on the distributions of single-equation estimators. In Hildenbrand, W. (ed.), Advances in Econometrics, pp. 109–122. Cambridge: Cambridge University Press, 1982.Google Scholar
3.Anderson, T.W., Kunitomo, N., & Morimune, K.. Comparing single-equation estimators in a simultaneous equation system. Econometric Theory 2 (1986): 1–32.CrossRefGoogle Scholar
4.Anderson, T.W., Kunitomo, N., & Sawa, T.. Evaluation of the distribution function of the limited information maximum likelihood estimator. Econometrica 50 (1982): 1009–1027.CrossRefGoogle Scholar
5.Anderson, T.W., Kunitomo, N., & Sawa, T.. Comparison of the densities of the TSLS and LIMLK estimators for simultaneous equations. In Adams, F.G. and Hickman, B.G. (eds.), Global Econometrics: Essays in Honor of Lawrence R. Klein, pp. 103–124. Cambridge, MA: MIT Press, 1983.Google Scholar
6.Anderson, T.W., Morimune, K., & Sawa, T.. The numerical values of some key parameters in econometric models. Journal of Econometrics 21 (1983): 229–243.CrossRefGoogle Scholar
7.Anderson, T.W. & Sawa, T.. Evaluation of the distribution function of the two-stage least squares estimate. Econometrica 47 (1979): 163–182.CrossRefGoogle Scholar
8.Fuller, W.A.Some properties of a modification of the limited information estimator. Econometrica 45 (1977): 939–953.CrossRefGoogle Scholar
9.Kadane, J.B.Comparison of Ar-class estimators when the disturbances are small. Econometrica 39 (1971): 723–737.CrossRefGoogle Scholar
10.Mariano, R.S. & Sawa, T.The exact finite-sample distribution of the limited-information maximum likelihood estimator in the case of two included endogenous variables. Journal of the American Statistical Association 67 (1972): 159–163.CrossRefGoogle Scholar
11.Richardson, D.H.The exact distribution of a structural coefficient estimator. Journal of the American Statistical Association 63 (1968): 1214–1226.CrossRefGoogle Scholar
12.Zaman, A.Estimators without moments: the case of the reciprocal of a normal mean. Journal of Econometrics 15 (1981): 289–298.CrossRefGoogle Scholar
13.Zellner, A.Estimation of functions of population means and regression coefficients including structural coefficients: a minimum expected loss (MELO) approach. Journal of Econometrics 8 (1978): 127–158.CrossRefGoogle Scholar
14.Zellner, A. Canonical representation of linear structural econometric models, rank tests for identification and existence of estimators' moments. In Karlin, S., Amemiya, T., and Goodman, L.A. (eds.), Studies in Econometrics, Time Series, and Multivariate Statistics, pp. 227–240. New York: Academic Press, 1983.CrossRefGoogle Scholar