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ERA's: A New Approach to Small Sample Theory

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Abstract

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 [10]. 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 [10]. 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 [10], suggest that the approach offers considerable potential for empirical application in terms of its reliability, convenience and generality.

Suggested Citation

  • Peter C.B. Phillips, 1982. "ERA's: A New Approach to Small Sample Theory," Cowles Foundation Discussion Papers 645, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:645
    Note: CFP 573.
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    1. 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.
    2. 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 463-485, March.
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    Cited by:

    1. Pieter J. van der Sluis, 1997. "Post-Sample Prediction Tests for the Efficient Method of Moments," Tinbergen Institute Discussion Papers 97-054/4, Tinbergen Institute.
    2. Kalouptsidis, N. & Psaraki, V., 2010. "Approximations of choice probabilities in mixed logit models," European Journal of Operational Research, Elsevier, vol. 200(2), pages 529-535, January.
    3. Hong, Seung Hyun & Phillips, Peter C. B., 2010. "Testing Linearity in Cointegrating Relations With an Application to Purchasing Power Parity," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(1), pages 96-114.
    4. van der Klaauw, Bas & Koning, Ruud H, 2003. "Testing the Normality Assumption in the Sample Selection Model with an Application to Travel Demand," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(1), pages 31-42, January.
    5. John Crooker & Joseph Herriges, 2004. "Parametric and Semi-Nonparametric Estimation of Willingness-to-Pay in the Dichotomous Choice Contingent Valuation Framework," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 27(4), pages 451-480, April.
    6. Pieter J. Van Der Sluis, 1998. "Computationally attractive stability tests for the efficient method of moments," Econometrics Journal, Royal Economic Society, vol. 1(Conferenc), pages 203-227.
    7. Peter C.B. Phillips & R.C. Reiss, 1984. "Testing for Serial Correlation and Unit Roots Using a Computer Function Routine Bases on ERA's," Cowles Foundation Discussion Papers 721, Cowles Foundation for Research in Economics, Yale University.
    8. Andersen, Torben G. & Lund, Jesper, 1997. "Estimating continuous-time stochastic volatility models of the short-term interest rate," Journal of Econometrics, Elsevier, vol. 77(2), pages 343-377, April.
    9. Kristensen, Dennis & Shin, Yongseok, 2012. "Estimation of dynamic models with nonparametric simulated maximum likelihood," Journal of Econometrics, Elsevier, vol. 167(1), pages 76-94.
    10. Im, Jongho & Morikawa, Kosuke & Ha, Hyung-Tae, 2020. "A least squares-type density estimator using a polynomial function," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    11. van der Sluis Pieter J., 1997. "EmmPack 1.01: C/C++ Code for Use with Ox for Estimation of Univariate Stochastic Volatility Models with the Efficient Method of Moments," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 2(3), pages 1-20, October.
    12. A. Sancetta & Satchell, S.E., 2001. "Bernstein Approximations to the Copula Function and Portfolio Optimization," Cambridge Working Papers in Economics 0105, Faculty of Economics, University of Cambridge.
    13. M. Dolores de Prada & Luis M. Borge, 1997. "Some methods for comparing first-order asymptotically equivalent estimators," Investigaciones Economicas, Fundación SEPI, vol. 21(3), pages 473-500, September.
    14. Peter C.B. Phillips, 1983. "Finite Sample Econometrics Using ERA's," Cowles Foundation Discussion Papers 683, Cowles Foundation for Research in Economics, Yale University.
    15. repec:dgr:rugsom:00f37 is not listed on IDEAS

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