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An Alternative Asymptotic Analysis of Residual-Based Statistics

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  • Andreou, E.
  • Werker, B.J.M.

    (Tilburg University, Center for Economic Research)

Abstract

This paper offers an alternative technique to derive the limiting distribution of residual-based statistics or, more general, the limiting distribution of statistics with estimated nuisance parameters.This technique allows us to unify many known results on two-stage estimators and tests and we also derive new results.The technique is especially useful in situations where smoothness of the statistic of interest with respect to the parameters to be estimated does not hold or is difficult to establish, e.g., rank-based statistics.We essentially replace this differentiability condition with a distributional invariance property that is often satisfied in specification tests.Our results on statistics that have not been considered before all use nonparametric statistics.On the technical side, we provide a novel approach to the pre-estimation problem using Le Cam s third lemma.The resulting formula for the correction in the limiting variance as a result of pre-estimation some parameters is a simple expression involving some appropriate covariances.The regularity conditions required fairly minimal.Numerous examples show the strength and wide applicability of our approach.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2004-56.

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Date of creation: 2004
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Handle: RePEc:dgr:kubcen:200456

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Keywords: statistics; estimation; testing;

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  1. Jeganathan, P., 1995. "Some Aspects of Asymptotic Theory with Applications to Time Series Models," Econometric Theory, Cambridge University Press, vol. 11(05), pages 818-887, October.
  2. Keuzenkamp, H.A. & Magnus, J.R., 1995. "The significance of testing in econometrics," Open Access publications from Tilburg University urn:nbn:nl:ui:12-153235, Tilburg University.
  3. Drost, F.C. & Klaassen, C.A.J., 1997. "Efficient estimation in semiparametric GARCH models," Open Access publications from Tilburg University urn:nbn:nl:ui:12-74146, Tilburg University.
  4. Spanos,Aris, 1986. "Statistical Foundations of Econometric Modelling," Cambridge Books, Cambridge University Press, number 9780521269124.
  5. Kreiss Jens-Peter, 1987. "On Adaptive Estimation In Autoregressive Models When There Are Nuisance Functions," Statistics & Risk Modeling, De Gruyter, vol. 5(1-2), pages 59-76, February.
  6. repec:cup:etheor:v:11:y:1995:i:5:p:818-87 is not listed on IDEAS
  7. Jeganathan, P., 1999. "On Asymptotic Inference In Cointegrated Time Series With Fractionally Integrated Errors," Econometric Theory, Cambridge University Press, vol. 15(04), pages 583-621, August.
  8. Adrian Pagan, 1985. "Two Stage and Related Estimators and Their Applications," Cowles Foundation Discussion Papers 741, Cowles Foundation for Research in Economics, Yale University.
  9. Jushan Bai, 2003. "Testing Parametric Conditional Distributions of Dynamic Models," The Review of Economics and Statistics, MIT Press, vol. 85(3), pages 531-549, August.
  10. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, vol. 66(5), pages 1127-1162, September.
  11. Drost, Feike C & Werker, Bas J M, 2004. "Semiparametric Duration Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 22(1), pages 40-50, January.
  12. Bierens, H.J., 1989. "A consistent conditional moment test of functional form," Serie Research Memoranda 0064, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  13. Donald W. K. Andrews, 1997. "A Conditional Kolmogorov Test," Econometrica, Econometric Society, vol. 65(5), pages 1097-1128, September.
  14. Linton, Oliver, 1993. "Adaptive Estimation in ARCH Models," Econometric Theory, Cambridge University Press, vol. 9(04), pages 539-569, August.
  15. Marc Hallin & Bas Werker, 1998. "Optimal testing for semiparametric autoregressive models: from Gaussian Lagrange multipliers to regression rank scores and adaptive tests," ULB Institutional Repository 2013/2219, ULB -- Universite Libre de Bruxelles.
  16. Lundbergh, Stefan & Teräsvirta, Timo, 1998. "Evaluating GARCH models," Working Paper Series in Economics and Finance 292, Stockholm School of Economics, revised 03 May 1999.
  17. Andrews, Donald W. K., 1988. "Chi-square diagnostic tests for econometric models : Introduction and applications," Journal of Econometrics, Elsevier, vol. 37(1), pages 135-156, January.
  18. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
  19. Newey, Whitney K. & McFadden, Daniel, 1986. "Large sample estimation and hypothesis testing," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 36, pages 2111-2245 Elsevier.
  20. Pagan, Adrian & Vella, Frank, 1989. "Diagnostic Tests for Models Based on Individual Data: A Survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 4(S), pages S29-59, Supplemen.
  21. Drost, F.C. & Klaassen, C.A.J. & Werker, B.J.M., 1997. "Adaptive estimation in time-series models," Open Access publications from Tilburg University urn:nbn:nl:ui:12-74145, Tilburg University.
  22. Newey, Whitney K, 1985. "Maximum Likelihood Specification Testing and Conditional Moment Tests," Econometrica, Econometric Society, vol. 53(5), pages 1047-70, September.
  23. MacKinnon, James G, 1992. "Model Specification Tests and Artificial Regressions," Journal of Economic Literature, American Economic Association, vol. 30(1), pages 102-46, March.
  24. Marc Hallin & Bas Werker, 2003. "Semiparametric efficiency, distribution-freeness, and invariance," ULB Institutional Repository 2013/2119, ULB -- Universite Libre de Bruxelles.
  25. Anderson, T W & Sawa, Takamitsu, 1979. "Evaluation of the Distribution Function of the Two-Stage Least Squares Estimate," Econometrica, Econometric Society, vol. 47(1), pages 163-82, January.
  26. Jinyong Hahn & Guido Kuersteiner, 2002. "Asymptotically Unbiased Inference for a Dynamic Panel Model with Fixed Effects when Both "n" and "T" Are Large," Econometrica, Econometric Society, vol. 70(4), pages 1639-1657, July.
  27. Ploberger, Werner & Kramer, Walter, 1992. "The CUSUM Test with OLS Residuals," Econometrica, Econometric Society, vol. 60(2), pages 271-85, March.
  28. repec:cup:etheor:v:13:y:1997:i:5:p:692-745 is not listed on IDEAS
  29. repec:cup:etheor:v:9:y:1993:i:4:p:539-69 is not listed on IDEAS
  30. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
  31. Tauchen, George, 1985. "Diagnostic testing and evaluation of maximum likelihood models," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 415-443.
  32. Jeganathan, P., 1997. "On Asymptotic Inference in Linear Cointegrated Time Series Systems," Econometric Theory, Cambridge University Press, vol. 13(05), pages 692-745, October.
  33. Hallin, M. & Puri, M.L., 1992. "Rank Tests for Time Series Analysis , A Survey," Papers 9210, Universite Libre de Bruxelles - C.E.M.E..
  34. Powell, James L, 1983. "The Asymptotic Normality of Two-Stage Least Absolute Deviations Estimators," Econometrica, Econometric Society, vol. 51(5), pages 1569-75, September.
  35. Cotter, Kevin D., 1986. "Similarity of information and behavior with a pointwise convergence topology," Journal of Mathematical Economics, Elsevier, vol. 15(1), pages 25-38, February.
  36. Amemiya, Takeshi, 1982. "Two Stage Least Absolute Deviations Estimators," Econometrica, Econometric Society, vol. 50(3), pages 689-711, May.
  37. Andrew Chesher & Richard J. Smith, 1997. "Likelihood Ratio Specification Tests," Econometrica, Econometric Society, vol. 65(3), pages 627-646, May.
  38. Bera, Anil K. & Jarque, Carlos M., 1982. "Model specification tests : A simultaneous approach," Journal of Econometrics, Elsevier, vol. 20(1), pages 59-82, October.
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Cited by:
  1. de Goeij, Peter & Marquering, Wessel, 2005. "The generalized asymmetric dynamic covariance model," Finance Research Letters, Elsevier, vol. 2(2), pages 67-74, June.
  2. Alberto Abadie & Guido W. Imbens, 2009. "Matching on the Estimated Propensity Score," NBER Working Papers 15301, National Bureau of Economic Research, Inc.

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