Pre-testing for linear restrictions in a regression model with spherically symmetric disturbances

a b s t r a c tFor the linear regression model y = X β + , we assume that for a given positive definite scale matrix Σ, the error vector has a multivariate normal distribution and Σ has the inverted Wishart distribution. For under an orthogonal sub-space restriction H β = h, we propose restricted unbiased, preliminary test and Stein-type estimators of variance of the error term, for when the scale of the inverse Wishart distribution is assumed to be unknown. We compare the weighted quadratic risks of the underlying estimators and propose dominance pictures for them.

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“…This estimator has been considered by Clarke et al [11] and Giles [13,14]. Here the PTE depends on α.…”

Section: The Proposed Estimatorsmentioning

confidence: 95%

Improved variance estimation under sub-space restriction

Arashi

Tabatabaey

2009

Journal of Multivariate Analysis

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“…This is a significant result as it implies that irrespective of the model's structure, the optimal solution for the N(y,s 2 I m Â m ) problem is also optimal for all regression models with the same value of m. Even so, this theorem relies heavily on the normality of error assumption (see an earlier version of Danilov and Magnus (2004) for a discussion). There is an extensive literature suggesting that economic and financial data are often generated by non-normal distributions (see, for example, Giles, 1991). So, it is important to consider extension of the Equivalence Theorem to the non-normal case.…”

Section: Introductionmentioning

confidence: 99%

Estimation of regression coefficients of interest when other regression coefficients are of no interest: The case of non-normal errors

Zou

Wan

et al. 2007

Statistics & Probability Letters

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“…Some examples are Zellner (1976), Ullah and Zinde-Walsh (1984), Giles (1991), and Namba and Ohtani (2002). Although Srivastava and Ullah (1995) examined the sampling properties of R 2 and R 2 under a general nonnormal error distribution, their analysis is based on the large sample asymptotic expansions.…”

Section: Introductionmentioning

confidence: 99%

Exact Distributions of R2 and Adjusted R2 in a Linear Regression Model with Multivariate t Error Terms

Ohtani

Tanizaki

2004

JJSS

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In this paper we consider a linear regression model when error terms obey a multivariate t distribution, and examine the effects of departure from normality of error terms on the exact distributions of the coefficient of determination (say, R 2 ) and adjusted R 2 (say, R 2 ). We derive the exact formulas for the density function, distribution function and m-th moment, and perform numerical analysis based on the exact formulas. It is shown that the upward bias of R 2 gets serious and the standard error of R 2 gets large as the degrees of freedom of the multivariate t error distribution (say, ν0) get small. The confidence intervals of R 2 and R 2 are examined, and it is shown that when the values of ν0 and the parent coefficient of determination (say, Φ) are small, the upper confidence limits are very large, relative to the value of Φ.

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Pre-testing for linear restrictions in a regression model with spherically symmetric disturbances

Cited by 69 publications

References 19 publications

Improved variance estimation under sub-space restriction

Improved variance estimation under sub-space restriction

Estimation of regression coefficients of interest when other regression coefficients are of no interest: The case of non-normal errors

Exact Distributions of <i>R<sup>2</sup></i> and Adjusted <i>R<sup>2</sup></i> in a Linear Regression Model with Multivariate <i>t</i> Error Terms

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