IDEAS home Printed from https://ideas.repec.org/a/ecm/emetrp/v51y1983i5p1505-25.html
   My bibliography  Save this article

ERAs: A New Approach to Small Sample Theory

Author

Listed:
  • Phillips, Peter C B

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.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Phillips, Peter C B, 1983. "ERAs: A New Approach to Small Sample Theory," Econometrica, Econometric Society, vol. 51(5), pages 1505-1525, September.
  • Handle: RePEc:ecm:emetrp:v:51:y:1983:i:5:p:1505-25
    as

    Download full text from publisher

    File URL: http://links.jstor.org/sici?sici=0012-9682%28198309%2951%3A5%3C1505%3AEANATS%3E2.0.CO%3B2-K&origin=repec
    File Function: full text
    Download Restriction: Access to full text is restricted to JSTOR subscribers. See http://www.jstor.org for details.
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Kristensen, Dennis & Shin, Yongseok, 2012. "Estimation of dynamic models with nonparametric simulated maximum likelihood," Journal of Econometrics, Elsevier, vol. 167(1), pages 76-94.
    9. 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).
    10. 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.
    11. 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.
    12. Peter C.B. Phillips, 1983. "Finite Sample Econometrics Using ERA's," Cowles Foundation Discussion Papers 683, Cowles Foundation for Research in Economics, Yale University.
    13. repec:dgr:rugsom:00f37 is not listed on IDEAS

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Phillips, P. C. B., 1987. "Asymptotic Expansions in Nonstationary Vector Autoregressions," Econometric Theory, Cambridge University Press, vol. 3(1), pages 45-68, February.
    2. Mehlum, Halvor, 2004. "Exact Small Sample Properties of the Instrumental Variable Estimator. A View From a Different Angle," Memorandum 03/2004, Oslo University, Department of Economics.
    3. Kenneth D. West & David W. Wilcox, 1993. "Some evidence on finite sample behavior of an instrumental variables estimator of the linear quadratic inventory model," Finance and Economics Discussion Series 93-29, Board of Governors of the Federal Reserve System (U.S.).
    4. Müller, Ulrich K. & Wang, Yulong, 2019. "Nearly weighted risk minimal unbiased estimation," Journal of Econometrics, Elsevier, vol. 209(1), pages 18-34.
    5. Chengsi Zhang & Joel Clovis, 2009. "Modeling China Inflation Persistence," Annals of Economics and Finance, Society for AEF, vol. 10(1), pages 89-110, May.
    6. repec:ebl:ecbull:v:3:y:2006:i:27:p:1-10 is not listed on IDEAS
    7. Michael P. Murray, 2006. "Avoiding Invalid Instruments and Coping with Weak Instruments," Journal of Economic Perspectives, American Economic Association, vol. 20(4), pages 111-132, Fall.
    8. Phillips, P C B, 1986. "The Distribution of FIML in the Leading Case," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 27(1), pages 239-243, February.
    9. Andrews, Donald W.K. & Guggenberger, Patrik, 2012. "Asymptotics for LS, GLS, and feasible GLS statistics in an AR(1) model with conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 169(2), pages 196-210.
    10. Russell Davidson & James G. MacKinnon, 2008. "Bootstrap inference in a linear equation estimated by instrumental variables," Econometrics Journal, Royal Economic Society, vol. 11(3), pages 443-477, November.
    11. Reed, W. Robert & Zhu, Min, 2017. "On estimating long-run effects in models with lagged dependent variables," Economic Modelling, Elsevier, vol. 64(C), pages 302-311.
    12. Marsh, Patrick, 2001. "Edgeworth expansions in Gaussian autoregression," Statistics & Probability Letters, Elsevier, vol. 54(3), pages 233-241, October.
    13. Zivot, Eric & Startz, Richard & Nelson, Charles R, 1998. "Valid Confidence Intervals and Inference in the Presence of Weak Instruments," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 1119-1146, November.
    14. Donggyu Sul & Peter C. B. Phillips & Chi‐Young Choi, 2005. "Prewhitening Bias in HAC Estimation," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 67(4), pages 517-546, August.
    15. Paul A. Bekker & Jan van der Ploeg, 2000. "Instrumental Variable Estimation Based on Grouped Data," Econometric Society World Congress 2000 Contributed Papers 1862, Econometric Society.
    16. Phillips, Peter C.B., 2006. "A Remark On Bimodality And Weak Instrumentation In Structural Equation Estimation," Econometric Theory, Cambridge University Press, vol. 22(5), pages 947-960, October.
    17. Bruce E. Hansen, 1999. "The Grid Bootstrap And The Autoregressive Model," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 594-607, November.
    18. Russell Davidson & James G. MacKinnon, 2014. "Confidence sets based on inverting Anderson–Rubin tests," Econometrics Journal, Royal Economic Society, vol. 17(2), pages 39-58, June.
    19. Randolph G. K. Tan, 2000. "Finite-Sample Optimality of Tests in a Structural Equation," Econometric Society World Congress 2000 Contributed Papers 1853, Econometric Society.
    20. Aman Ullah & Yong Bao & Ru Zhang, 2014. "Moment Approximation for Unit Root Models with Nonnormal Errors," Working Papers 201401, University of California at Riverside, Department of Economics.
    21. Lui, Yiu Lim & Xiao, Weilin & Yu, Jun, 2018. "The Grid Bootstrap for Continuous Time Models," Economics and Statistics Working Papers 20-2018, Singapore Management University, School of Economics.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ecm:emetrp:v:51:y:1983:i:5:p:1505-25. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wiley Content Delivery). General contact details of provider: https://edirc.repec.org/data/essssea.html .

    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 CitEc recognized a reference but did not link an item in RePEc 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 RePEc Author Service 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.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.