On the Exact Statistical Distribution of Econometric Estimators and Test Statistics

Yong Bao, Xiaotian Liu () and Aman Ullah
Additional contact information
Xiaotian Liu: Purdue University

No 202014, Working Papers from University of California at Riverside, Department of Economics

Abstract: Barry Arnold has made many fundamental and innovative contributions in different areas of statistics and econometrics, including estimation and inference,distribution theory, Bayesian inference, order statistics, income inequality measures, and characterization problems. His extensive work in the area of distribution theory include studies on income distributions and Lorenz curves, the exact sampling distribution theory of test statistics, and the characterization of distributions. In our paper here we consider the problem of developing exact sampling distributions of various econometric and statistical estimators and test statistics. The motivation stems from the fact that inference procedures based on the asymptotic distributions may provide misleading results if the sample size is small or moderately large. In view of this we develop a unified procedure by first observing that a large number of econometric and statistical estimators can be written as ratios of quadratic forms. Their distributions can then be straightforwardly analyzed by using Imhof’s (1961) method. We show the applications of this procedure to develop the distribution of some commonly used statistics in applied work. The exact results developed will be helpful for practitioners to conduct appropriate inference for any given size of the sample data.

Keywords: Exact Distribution; Sharp Ratio; Coeficcient of Variation; Durbi-Watson Test; Moran Test; Imhof Distribution; R-square (search for similar items in EconPapers)
Pages: 14 Pages
Date: 2020-01, Revised 2020-06
New Economics Papers: this item is included in nep-ecm
References: View references in EconPapers View complete reference list from CitEc
Citations:

Forthcoming

Downloads: (external link)
https://economics.ucr.edu/repec/ucr/wpaper/202014.pdf First version, 2020 (application/pdf)
https://economics.ucr.edu/repec/ucr/wpaper/202014R.pdf Revised version, 2020 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ucr:wpaper:202014

Access Statistics for this paper

More papers in Working Papers from University of California at Riverside, Department of Economics Contact information at EDIRC.
Bibliographic data for series maintained by Kelvin Mac ().