An asymptotic expansion for the distribution of the determinant of a multivariate quadratic form in a normal sample
β Scribed by Takesi Hayakawa
- Publisher
- Springer Japan
- Year
- 1973
- Tongue
- English
- Weight
- 478 KB
- Volume
- 25
- Category
- Article
- ISSN
- 0020-3157
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π SIMILAR VOLUMES
Consider the quadratic form Z=Y H (XL X H ) &1 Y where Y is a p\_m complex Gaussian matrix, X is an independent p\_n complex Gaussian matrix, L is a Hermitian positive definite matrix, and m p n. The distribution of Z has been studied for over 30 years due to its importance in certain multivariate s
Let the column vectors of X: M\_N, M<N, be distributed as independent complex normal vectors with the same covariance matrix 7. Then the usual quadratic form in the complex normal vectors is denoted by Z=XLX H where L: N\_N is a positive definite hermitian matrix. This paper deals with a representat
In this paper a series representation of the joint density and the joint distribution of a quadratic form and a linear form in normal variables is developed. The expansion makes use of Laguerre polynomials. As an example the calculation of the joint distribution of the mean and the sample variance i