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Score Test for the Covariance Matrix of the Elliptic t-Distribution

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  • Sutradhar, B. C.

Abstract

Let x1, ..., xj, ..., xn be n independent realizations of a p-dimensional random variable X which has the elliptical t-distribution of the form g(x) = K([nu], p) [Sigma]-1/2 [([nu] - 2) + (x - [theta])' [Sigma]-1(x - [theta])]-([nu] + p)/2, where [theta] and [Sigma] denote the p - 1 location vector and p - p covariance matrix, respectively, and [nu] is the degrees of freedom of the distribution. This paper develops an asymptotically locally most powerful test for testing the covariance matrix [Sigma] = [Sigma]0, based on Neyman's approach. The proposed test statistic has asymptotically [chi]2 distribution with [gamma] degrees of freedom, where [gamma] is the number of independent restrictions over the parameters, specified under the null hypothesis.

Suggested Citation

  • Sutradhar, B. C., 1993. "Score Test for the Covariance Matrix of the Elliptic t-Distribution," Journal of Multivariate Analysis, Elsevier, vol. 46(1), pages 1-12, July.
    • Handle: RePEc:eee:jmvana:v:46:y:1993:i:1:p:1-12
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    Cited by:

    1. Galea, Manuel & de Castro, Mário, 2017. "Robust inference in a linear functional model with replications using the t distribution," Journal of Multivariate Analysis, Elsevier, vol. 160(C), pages 134-145.
    2. Manuel Galea & David Cademartori & Roberto Curci & Alonso Molina, 2020. "Robust Inference in the Capital Asset Pricing Model Using the Multivariate t -distribution," JRFM, MDPI, vol. 13(6), pages 1-22, June.

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