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Exact optimal inference in regression models under heteroskedasticity and non-normality of unknown form

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Author Info

  • Dufour, Jean-Marie
  • Taamouti, Abderrahim

Abstract

Simple point-optimal sign-based tests are developed for inference on linear and nonlinear regression models with non-Gaussian heteroskedastic errors. The tests are exact, distribution-free, robust to heteroskedasticity of unknown form, and may be inverted to build confidence regions for the parameters of the regression function. Since point-optimal sign tests depend on the alternative hypothesis considered, an adaptive approach based on a split-sample technique is proposed in order to choose an alternative that brings power close to the power envelope. The performance of the proposed quasi-point-optimal sign tests with respect to size and power is assessed in a Monte Carlo study. The power of quasi-point-optimal sign tests is typically close to the power envelope, when approximately 10% of the sample is used to estimate the alternative and the remaining sample to compute the test statistic. Further, the proposed procedures perform much better than common least-squares-based tests which are supposed to be robust against heteroskedasticity.

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Bibliographic Info

Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

Volume (Year): 54 (2010)
Issue (Month): 11 (November)
Pages: 2532-2553

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Handle: RePEc:eee:csdana:v:54:y:2010:i:11:p:2532-2553

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Web page: http://www.elsevier.com/locate/csda

Related research

Keywords: Sign test Point-optimal test Nonlinear model Heteroskedasticity Exact inference Distribution-free Power envelope Split-sample Adaptive method Projection;

References

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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.:
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  1. Jean-Marie Dufour, 2005. "Monte Carlo tests with nuisance parameters: a general approach to finite-sample inference and non-standard asymptotics," CIRANO Working Papers 2005s-02, CIRANO.
  2. ABDELKHALEK, Touhami & DUFOUR, Jean-Marie, 1997. "Statistical Inference for Computable General Equilibrium Models with Application to a Model of the Moroccan Economy," Cahiers de recherche 9713, Universite de Montreal, Departement de sciences economiques.
  3. DUFOUR, Jean-Marie & TAAMOUTI, Mohamed, 2003. "Projection-Based Statistical Inference in Linear Structural Models with Possibly Weak Instruments," Cahiers de recherche 08-2003, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  4. Dufour, J.M. & Campbell, B., 1993. "Exact Nonparametric Orthogonality and Random Walk Tests," Cahiers de recherche 9326, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  5. Jean-Marie Dufour & Jan F. Kiviet, 1998. "Exact Inference Methods for First-Order Autoregressive Distributed Lag Models," Econometrica, Econometric Society, vol. 66(1), pages 79-104, January.
  6. Campbell, Bryan & Dufour, Jean-Marie, 1997. "Exact Nonparametric Tests of Orthogonality and Random Walk in the Presence of a Drift Parameter," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(1), pages 151-73, February.
  7. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-36, July.
  8. Dufour, Jean-Marie & Jasiak, Joann, 2001. "Finite Sample Limited Information Inference Methods for Structural Equations and Models with Generated Regressors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(3), pages 815-43, August.
  9. Gerard, Patrick D. & Schucany, William R., 2007. "An enhanced sign test for dependent binary data with small numbers of clusters," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4622-4632, May.
  10. N. Gregory Mankiw & Matthew D. Shapiro, 1985. "Do We Reject Too Often? Small Sample Properties of Tests of Rational Expectations Models," NBER Technical Working Papers 0051, National Bureau of Economic Research, Inc.
  11. Dufour, J-M., 1988. "Non-Uniform Bounds For Nonparametric T Tests," Cahiers de recherche 8820, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  12. Liang, Tachen & Huang, Wen-Tao & Yang, Kun-Cheng, 2008. "Locally optimal tests for exponential distributions with type-I censoring," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3603-3615, March.
  13. Dufour, Jean-Marie & King, Maxwell L., 1991. "Optimal invariant tests for the autocorrelation coefficient in linear regressions with stationary or nonstationary AR(1) errors," Journal of Econometrics, Elsevier, vol. 47(1), pages 115-143, January.
  14. Jansson, Michael, 2005. "Point optimal tests of the null hypothesis of cointegration," Journal of Econometrics, Elsevier, vol. 124(1), pages 187-201, January.
  15. Capanu, Marinela & Jones, Gregory A. & Randles, Ronald H., 2006. "Testing for preference using a sum of Wilcoxon signed rank statistics," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 793-796, November.
  16. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-38, May.
  17. Emma Iglesias & Jean Marie Dufour, 2004. "Finite Sample and Optimal Inference in Possibly Nonstationary ARCH Models with Gaussian and Heavy-Tailed Errors," Econometric Society 2004 North American Summer Meetings 161, Econometric Society.
  18. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-62, November.
  19. Begum, Nelufa & King, Maxwell L., 2005. "Most mean powerful test of a composite null against a composite alternative," Computational Statistics & Data Analysis, Elsevier, vol. 49(4), pages 1079-1104, June.
  20. Jean-Marie Dufour, 2003. "Identification, weak instruments, and statistical inference in econometrics," Canadian Journal of Economics, Canadian Economics Association, vol. 36(4), pages 767-808, November.
  21. Jean-Marie Dufour, 1997. "Some Impossibility Theorems in Econometrics with Applications to Structural and Dynamic Models," Econometrica, Econometric Society, vol. 65(6), pages 1365-1388, November.
  22. DUFOUR, Jean-Marie, 2003. "Identification, Weak Instruments and Statistical Inference in Econometrics," Cahiers de recherche 10-2003, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
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Cited by:
  1. Gossner, Olivier & Schlag, Karl H., 2013. "Finite-sample exact tests for linear regressions with bounded dependent variables," Journal of Econometrics, Elsevier, vol. 177(1), pages 75-84.

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