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

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Author Info
Jean-Marie Dufour ()
Abderrahim Taamouti ()

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Abstract

In this paper, we derive simple point-optimal sign-based tests in the context of linear and nonlinear regression models with fixed regressors. These tests are exact, distribution-free, robust against heteroskedasticity of unknown form, and they may be inverted to obtain confidence regions for the vector of unknown parameters. Since the point-optimal sign tests depend on the alternative hypothesis, we propose an adaptive approach based on split-sample techniques in order to choose an alternative such that the power of point-optimal sign tests is close to the power envelope. The simulation results show that when using approximately 10% of sample to estimate the alternative and the rest to calculate the test statistic, the power of point-optimal sign test is typically close to the power envelope. We present a Monte Carlo study to assess the performance of the proposed “quasi”-point-optimal sign test by comparing its size and power to those of some common tests which are supposed to be robust against heteroskedasticity. The results show that our procedures are superior.

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Paper provided by Universidad Carlos III, Departamento de Economía in its series Economics Working Papers with number we086027.

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Date of creation: Nov 2008
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Handle: RePEc:cte:werepe:we086027

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

Find related papers by JEL classification:
C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Statistical Simulation Methods
C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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References listed on IDEAS
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  1. DUFOUR, Jean-Marie, 2003. "Identification, Weak Instruments and Statistical Inference in Econometrics," Cahiers de recherche 2003-12, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
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  2. 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. [Downloadable!] (restricted)
  3. Benjamin M. Friedman & David I. Laibson, 1989. "Economic Implications of Extraordinary Movements in Stock Prices," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 20(1989-2), pages 137-190. [Downloadable!]
  4. Jean-Marie Dufour & Mohamed Taamouti, 2005. "Projection-Based Statistical Inference in Linear Structural Models with Possibly Weak Instruments," Econometrica, Econometric Society, vol. 73(4), pages 1351-1365, 07. [Downloadable!] (restricted)
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  5. 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.
  6. Gregory Mankiw, N. & Shapiro, Matthew D., 1986. "Do we reject too often? : Small sample properties of tests of rational expectations models," Economics Letters, Elsevier, vol. 20(2), pages 139-145. [Downloadable!] (restricted)
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  7. Wright, Jonathan H, 2000. "Alternative Variance-Ratio Tests Using Ranks and Signs," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(1), pages 1-9, January.
  8. 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. [Downloadable!] (restricted)
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  9. 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.
  10. Jansson, Michael, 2005. "Point optimal tests of the null hypothesis of cointegration," Journal of Econometrics, Elsevier, vol. 124(1), pages 187-201, January. [Downloadable!] (restricted)
  11. Touhami Abdelkhalek & Jean-Marie Dufour, 1998. "Statistical Inference For Computable General Equilibrium Models, With Application To A Model Of The Moroccan Economy," The Review of Economics and Statistics, MIT Press, vol. 80(4), pages 520-534, November. [Downloadable!] (restricted)
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  12. Campbell, Bryan & Dufour, Jean-Marie, 1995. "Exact Nonparametric Orthogonality and Random Walk Tests," The Review of Economics and Statistics, MIT Press, vol. 77(1), pages 1-16, February. [Downloadable!] (restricted)
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  13. 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.
  14. 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.
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  15. Dufour, J.M. & Kiviet, J.F., 1995. "Exact Inference Methods for First-Order Autoregressive Distributed Lag Models," Cahiers de recherche 9547, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
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