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Nonlinear Hypotheses, Inequality Restrictions, and Non-nested Hypotheses: Exact Simultaneous Tests in Linear Regressions

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Dufour, Jean-Marie

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Abstract

In the classical linear model, comparison of two arbitrary hypotheses on the regression coefficients is considered. Problems involving nonlinear hypotheses, inequality restrictions, or non-nested hypotheses are included. Exact bounds on the null distribution of likelihood ratio statistics are derived (based on the central Fisher distribution). As a special case, a bounds test similar to the Durbin-Watson test is proposed. Multiple testing problems are studied: the bounds obtained for a single pair of hypotheses are shown to enjoy a simultaneity property that allows combination of any number of tests. This result extends to nonlinear hypotheses a well-known result given by H. Scheffe for linear hypotheses. A method of building bounds-induced tests is suggested. Copyright 1989 by The Econometric Society.

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Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 57 (1989)
Issue (Month): 2 (March)
Pages: 335-55
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Handle: RePEc:ecm:emetrp:v:57:y:1989:i:2:p:335-55

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  1. Jean-Marie Dufour & Abdeljelil Farhat, 2001. "Exact Nonparametric Two-Sample Homogeneity Tests for Possibly Discrete Distributions," CIRANO Working Papers 2001s-56, CIRANO. [Downloadable!]
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  2. J. Dufour, . "Some Impossibility Theorems in Econometrics with Applications to Instrumental Variables, Dynamic Models and Cointegration," Sonderforschungsbereich 373 1995-27, Humboldt Universitaet Berlin.
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  3. 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. [Downloadable!]
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  4. Jean-Marie Dufour & Joanna Jasiak, 2000. "Finite Sample Inference Methods for Simultaneous Equations and Models with Unobserved and Generated Regressors," Econometric Society World Congress 2000 Contributed Papers 1536, Econometric Society. [Downloadable!]
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  5. Jean-Marie Dufour & Lynda Khalaf, 2000. "Simulation Based Finite and Large Sample Tests in Multivariate Regressions," CIRANO Working Papers 2000s-15, CIRANO. [Downloadable!]
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  6. Jean-Marie Dufour & Olivier Torrès, 2000. "Markovian Processes, Two-Sided Autoregressions and Finite-Sample Inference for Stationary and Nonstationary Autoregressive Processes," CIRANO Working Papers 2000s-17, CIRANO. [Downloadable!]
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  7. Denis Bolduc & Lynda Khalaf & Clément Yélou, 2005. "Identification Robust Confidence Sets Methods for Inference on Parameter Ratios and their Application to Estimating Value-of-Time," Computing in Economics and Finance 2005 48, Society for Computational Economics. [Downloadable!]
  8. 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. [Downloadable!]
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