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

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  • Dufour, Jean-Marie
  • Taamouti, Abderrahim

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 de Madrid in its series Open Access publications from Universidad Carlos III de Madrid with number info:hdl:10016/3201.

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Handle: RePEc:ner:carlos:info:hdl:10016/3201

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Web page: http://www.uc3m.es

Related research

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

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  1. 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.
  2. 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.
  3. Donald W.K. Andrews & James H. Stock, 2005. "Inference with Weak Instruments," NBER Technical Working Papers 0313, National Bureau of Economic Research, Inc.
  4. repec:mtl:montec:10-2003 is not listed on IDEAS
  5. 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.
  6. Campbell, B. & Dufour, J.M., 1994. "Excat Nonparametric Tests of Orthogonality and Random Walk in the Presence of a Drift Parameter," Cahiers de recherche 9407, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  7. 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(2), pages 137-190.
  8. 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.
  9. Dufour, J.M. & Kiviet, J.F., 1995. "Exact Inference Methods for First-Order Autoregressive Distributed Lag Models," Cahiers de recherche 9547, Universite de Montreal, Departement de sciences economiques.
  10. 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.
  11. 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.
  12. Jansson, Michael, 2005. "Point optimal tests of the null hypothesis of cointegration," Journal of Econometrics, Elsevier, vol. 124(1), pages 187-201, January.
  13. 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.
  14. 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.
  15. 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.
  16. 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.
  17. 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.
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