ERA's: A New Approach to Small Sample Theory
This article proposes a new approach to small sample theory that achieves a meaningful integration of earlier directions of research in this field. The approach centers on the constructive technique of approximating distributions developed recently by the author in . This technique utilizes extended rational approximants (ERA's) which methods (such as those based on asymptotic expansions) and which simultaneously blend information from diverse analytic, numerical and experimental sources. The first part of the article explores the general theory of approximation of continuous probability distributions by means of ERA's. Existence, characterization, error bound and uniqueness for the convergence result obtained earlier in . Some further aspects of finding ERA's by modifications to multiple-point Pade approximants are presented and the new approach is applied to the non-circular serial correlation coefficient. The results of this application demonstrate how ERA's provide systematic improvements over Edgeworth and saddlepoint techniques. These results, taken with those of the earlier article , suggest that the approach offers considerable potential for empirical application in terms of its reliability, convenience and generality.
|Date of creation:||Aug 1982|
|Date of revision:|
|Publication status:||Published in Econometrica (September 1983), 51(5): 1506-1525|
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- Peter C.B. Phillips, 1982.
"Exact Small Sample Theory in the Simultaneous Equations Model,"
Cowles Foundation Discussion Papers
621, Cowles Foundation for Research in Economics, Yale University.
- Phillips, P.C.B., 1983. "Exact small sample theory in the simultaneous equations model," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 1, chapter 8, pages 449-516 Elsevier.
- Phillips, Peter C B, 1977. "Approximations to Some Finite Sample Distributions Associated with a First-Order Stochastic Difference Equation," Econometrica, Econometric Society, vol. 45(2), pages 463-85, March.
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