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Activity Number:
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431
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Type:
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Contributed
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Date/Time:
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Thursday, August 12, 2004 : 10:30 AM to 12:20 PM
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Sponsor:
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Business and Economics Statistics Section
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| Abstract - #300377 |
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Title:
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Inconsistency of Estimate of the Degree of Freedom of Multivariate Student-t Disturbances in Linear Regression Models
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Author(s):
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Wai C. Ip*+
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Companies:
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Hong Kong Polytechnic University
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Address:
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Dept. of Applied Mathematics, Kowloon, HK, Hong Kong
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Keywords:
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characteristic function ; Chebychev's inequality ; variance
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Abstract:
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In most theoretical and applied research on linear regression models, disturbance terms are traditionally assumed to have a normal distribution. However, it is well known in practical situations that disturbance terms can have distributions with fatter tails than a normal distribution. In cases where the multivariate student-t distribution is employed, the variance of the estimates and confidence intervals of regression coefficients will depend on the degree of freedom of the t-distribution. Thus, these are not computable in practice where the degree of freedom is unknown. A moment estimator has been suggested in the literature for the degree of freedom of the jointly multivariate student-t distribution of the disturbances in a linear regression. We will show that the distribution of the moment estimate is independent of the true value of the degree of freedom and the moment estimate converges to infinite in probability as the sample size goes to infinite. Our results show that the moment estimate does not provide any information on the degree of freedom of the disturbance distribution.
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