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Classes of Similar Regions and Their Power Properties for Some Econometric Testing Problems

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  • Hillier, Grant H.

Abstract

In an hypothesis testing problem involving nuisance parameters for which boundedly complete sufficient statistics exist under the null hypothesis, the class of all similar regions for the problem is characterized by the conditional distribution of the data given these sufficient statistics. If there exists a one-to-one transformation y → ( t, u ) of the data, y , to the sufficient statistic, t , and a second vector of statistics, u , that is independent of t under the null hypothesis, then the statistic u itself characterizes the class of similar regions. This paper applies this idea to five testing problems of interest in econometrics. In each case we obtain the density of the relevant statistic under the null hypothesis, when it is free of nuisance parameters, and under the alternative. Using the density under the alternative, we discuss the power properties of the class of similar tests for each problem. Other applications are also suggested.

Suggested Citation

  • Hillier, Grant H., 1987. "Classes of Similar Regions and Their Power Properties for Some Econometric Testing Problems," Econometric Theory, Cambridge University Press, vol. 3(01), pages 1-44, February.
  • Handle: RePEc:cup:etheor:v:3:y:1987:i:01:p:1-44_00
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    Cited by:

    1. Kiviet, Jan F. & Dufour, Jean-Marie, 1997. "Exact tests in single equation autoregressive distributed lag models," Journal of Econometrics, Elsevier, vol. 80(2), pages 325-353, October.
    2. Maxwell L. King & Sivagowry Sriananthakumar, 2015. "Point Optimal Testing: A Survey of the Post 1987 Literature," Monash Econometrics and Business Statistics Working Papers 5/15, Monash University, Department of Econometrics and Business Statistics.
    3. Forchini, Giovanni, 2005. "Optimal weighted average power similar tests for the covariance structure in the linear regression model," Journal of Econometrics, Elsevier, vol. 124(2), pages 253-267, February.
    4. Patrick Marsh, "undated". "A Measure of Distance for the Unit Root Hypothesis," Discussion Papers 05/02, Department of Economics, University of York.
    5. Hillier, Grant, 2009. "On The Conditional Likelihood Ratio Test For Several Parameters In Iv Regression," Econometric Theory, Cambridge University Press, vol. 25(02), pages 305-335, April.
    6. Giovanni Forchini & Patrick Marsh, "undated". "Exact Inference for the Unit Root Hypothesis," Discussion Papers 00/54, Department of Economics, University of York.
    7. G. Forchini, 2005. "Some Properties of Tests for Possibly Unidentified Parameters," Monash Econometrics and Business Statistics Working Papers 21/05, Monash University, Department of Econometrics and Business Statistics.
    8. Giovanni Forchini, "undated". "The Geometry of Similar Tests for Structural Change," Discussion Papers 00/55, Department of Economics, University of York.
    9. 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.
    10. Patrick Marsh, "undated". "Nonparametric Likelihood Ratio Tests," Discussion Papers 00/56, Department of Economics, University of York.
    11. Giovanni Forchini, 2005. "Weighted Average Power Similar Tests for Structural Change for the Gaussian Linear Regression Model," Monash Econometrics and Business Statistics Working Papers 20/05, Monash University, Department of Econometrics and Business Statistics.
    12. Hillier, Grant, 2009. "Exact Properties Of The Conditional Likelihood Ratio Test In An Iv Regression Model," Econometric Theory, Cambridge University Press, vol. 25(04), pages 915-957, August.
    13. Martellosio, Federico, 2008. "Power Properties of Invariant Tests for Spatial Autocorrelation in Linear Regression," MPRA Paper 7255, University Library of Munich, Germany.
    14. Patrick Marsh, 2006. "Constructing Optimal Tests on a Lagged Dependent Variable," Discussion Papers 06/19, Department of Economics, University of York.

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