A New Approach to Small Sample Theory
AbstractIt is argued that an integral part of the process by which the results of small sample theory can be transmitted to the applied econometrician will in the future be played by reliable direct approximation to the sampling and posterior distributions that are of interest in the precise setting of the model and the data set with which the investigator is working. The purpose of this paper is to introduce a new technique of approximating distributions which is sufficiently general to be widely used and is developed in very general terms and should be widely applicable in mathematical statistics and econometrics. It has the advantage, unlike existing methods that are based on asymptotic expansions, of readily incorporating extraneous information on the distribution; even qualitative or soft quantitative information, such as that based on Monte Carlo experiments. It is shown that best uniform approximants in the form of rational functions exist for a general class of probability density functions. Characterization, uniqueness and convergence theorems for these approximations are given. An operational procedure for extracting rational approximants with good global behavior is devised and is based on modifying multiple-point Pade approximants which will typically utilize purely local information about the behavior of the body and the tails of the distribution. The new procedure is applied to a simple simultaneous equation estimator and gives exceptionally accurate results even for tiny values of the concentration parameter.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 608.
Length: 85 pages
Date of creation: Oct 1981
Date of revision:
Contact details of provider:
Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
Fax: (203) 432-6167
Web page: http://cowles.econ.yale.edu/
More information through EDIRC
Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Peter C.B. Phillips, 1978. "A Note on the Saddlepoint Approximation in the First Order Non-Circular Autoregression," Cowles Foundation Discussion Papers 487, Cowles Foundation for Research in Economics, Yale University.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Glena Ames).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.