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

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Author Info
Hillier, Grant H.

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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.

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Publisher Info
Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 3 (1987)
Issue (Month): 01 (February)
Pages: 1-44
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Handle: RePEc:cup:etheor:v:3:y:1987:i:01:p:1-44_00

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  1. Patrick Marsh, . "A Measure of Distance for the Unit Root Hypothesis," Discussion Papers 05/02, Department of Economics, University of York. [Downloadable!]
  2. Giovanni Forchini, . "The Geometry of Similar Tests for Structural Change," Discussion Papers 00/55, Department of Economics, University of York. [Downloadable!]
  3. 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. [Downloadable!]
  4. Martellosio, Federico, 2006. "Power Properties of Invariant Tests for Spatial Autocorrelation in Linear Regression," MPRA Paper 7255, University Library of Munich, Germany, revised Aug 2008. [Downloadable!]
  5. Grant Hillier, 2006. "On the conditional likelihood ratio test for several parameters in IV regression," CeMMAP working papers CWP26/06, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
    Other versions:
  6. Giovanni Forchini & Patrick Marsh, . "Exact Inference for the Unit Root Hypothesis," Discussion Papers 00/54, Department of Economics, University of York. [Downloadable!]
  7. Patrick Marsh, 2006. "Constructing Optimal Tests on a Lagged Dependent Variable," Discussion Papers 06/19, Department of Economics, University of York. [Downloadable!]
  8. Patrick Marsh, . "Nonparametric Likelihood Ratio Tests," Discussion Papers 00/56, Department of Economics, University of York. [Downloadable!]
  9. 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. [Downloadable!]
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