Book contents
- Frontmatter
- Contents
- List of figures
- List of tables
- List of contributors
- Preface
- Acknowledgements
- Michael Magdalinos 1949–2002
- Introduction
- 1 Conditional Heteroskedasticity Models with Pearson Disturbances
- 2 The Instrumental Variables Method Revisited: On the Nature and Choice of Optimal Instruments
- 3 Nagar-Type Moment Approximations in Simultaneous Equation Models: Some Further Results
- 4 Local GEL Methods for Conditional Moment Restrictions
- 5 Limit Theory for Moderate Deviations From a Unit Root Under Weak Dependence
- 6 The Structure of Multiparameter Tests
- 7 Cornish-Fisher Size Corrected t and F Statistics for the Linear Regression Model with Heteroscedastic Errors
- 8 Non-Parametric Specification Testing of Non-Nested Econometric Models
- 9 Testing for Autocorrelation in Systems of Equations
- 10 Alternative Approaches to Estimation and Inference in Large Multifactor Panels: Small Sample Results with an Application to Modelling Asset Returns
- 11 Judging Contending Estimators by Simulation: Tournaments in Dynamic Panel Data Models
- 12 A Statistical Proof of the Transformation Theorem
- 13 On the Joint Density of the Sum and Sum of Squares of Non-Negative Random Variables
- 14 Conditional Response Analysis
- References
- Index
7 - Cornish-Fisher Size Corrected t and F Statistics for the Linear Regression Model with Heteroscedastic Errors
Published online by Cambridge University Press: 22 September 2009
- Frontmatter
- Contents
- List of figures
- List of tables
- List of contributors
- Preface
- Acknowledgements
- Michael Magdalinos 1949–2002
- Introduction
- 1 Conditional Heteroskedasticity Models with Pearson Disturbances
- 2 The Instrumental Variables Method Revisited: On the Nature and Choice of Optimal Instruments
- 3 Nagar-Type Moment Approximations in Simultaneous Equation Models: Some Further Results
- 4 Local GEL Methods for Conditional Moment Restrictions
- 5 Limit Theory for Moderate Deviations From a Unit Root Under Weak Dependence
- 6 The Structure of Multiparameter Tests
- 7 Cornish-Fisher Size Corrected t and F Statistics for the Linear Regression Model with Heteroscedastic Errors
- 8 Non-Parametric Specification Testing of Non-Nested Econometric Models
- 9 Testing for Autocorrelation in Systems of Equations
- 10 Alternative Approaches to Estimation and Inference in Large Multifactor Panels: Small Sample Results with an Application to Modelling Asset Returns
- 11 Judging Contending Estimators by Simulation: Tournaments in Dynamic Panel Data Models
- 12 A Statistical Proof of the Transformation Theorem
- 13 On the Joint Density of the Sum and Sum of Squares of Non-Negative Random Variables
- 14 Conditional Response Analysis
- References
- Index
Summary
Introduction
The linear regression model with a nonscalar error covariance matrix is usually estimated by Generalized Least Squares (GLS). Conventional F and t-testing procedures of any linear hypotheses on the parameters for this model is justified under the implicit assumption that the sample size is large enough to permit inference on the parameters estimates based on the chi-square or normal distributions. However, the possibility of erroneous inferences in finite samples is always present, and it can be attributed to the existence of considerable discrepancy between the actual and the nominal size of the asymptotic chi-square or normal tests. Since the differences between the actual and nominal size tend to be large in finite samples, compared with the differences in power (see Rothenberg, 1982), size corrections are suggested to eliminate most of the probability of conflict among the alternative testing procedures (see Rothenberg, 1984b, 1988, and Magdalinos and Symeonides, 1995). In particular, Rothenberg (1984b, 1988) derived general formulae giving the Edgeworth-corrected critical values for the Wald and t-test statistics based on Edgeworth expansions of their corresponding asymptotic, chi-square and normal distributions, respectively. This is done for a wide class of regression models used in practice. Instead of using the asymptotic form of the tests, Magdalinos and Symeonides (1995, 1996) recommended to use the degrees of freedom adjusted forms of the above statistics and derived expansions in terms of the F and t distributions, respectively.
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- Chapter
- Information
- The Refinement of Econometric Estimation and Test ProceduresFinite Sample and Asymptotic Analysis, pp. 173 - 204Publisher: Cambridge University PressPrint publication year: 2007
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