The density of a quadratic form in a vector uniformly distributed on the n-sphere

Econometric Theory

Volumn 17, Issue 1, 2001, Pages 1-28

  Hillier, Grant ^a  

^a UNIVERSITY OF SOUTHAMPTON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035625024     PISSN: 02664666     EISSN: None     Source Type: Journal    
DOI: 10.1017/S026646660117101X     Document Type: Article

References (17)

1. Abramowitz, M. & I. Stegun (1964) Handbook of Mathematical Functions. New York: Dover.
2. Anderson, T.W. (1971) The Statistical Analysis of Time Series. New York: Wiley.
3. Henshaw, R.C. (1966) Testing single-equation least squares regression models for autocorrelated disturbances. Econometrica 34, 646-660.
4. Herz, C.S. (1955) Bessel functions of matrix argument. Annals of Mathematics 61 (3), 474-523.
5. James, A.T. (1961a) The distribution of noncentral means with known covariance. Annals of Mathematical Statistics 32, 874-882.
6. James, A.T. (1961b) Zonal polynomials of the real positive definite symmetric matrices. Annals of Mathematics 74, 456-469.
7. James, A.T. (1964) Distributions of matrix variates and latent roots derived from normal samples. Annals of Mathematical Statistics 35, 475-501.
8. Koopmans, T. (1942) Serial correlation and quadratic forms in normal variables. Annals of Mathematical Statistics 12, 14-33.
9. Muirhead, R.J. (1982) Aspects of Multivariate Statistical Theory. New York: Wiley.
10. Mulholland, H.P. (1965) On the degree of smoothness and on singularities in distributions of statistical functions. Proceedings of the Cambridge Philosophical Society 61, 721-739.
11. Mulholland, H.P. (1970) On singularities of sampling distributions, in particular for ratios of quadratic forms. Biometrika 57, 155-174.
12. Phillips, P.C.B. (1986) The exact distribution of the Wald statistic. Econometrica 54, 881-895.
13. Rainville, E.D. (1960) Special Functions. New York: Macmillan.
14. Saldanha, N.C. & C. Tomei (1996) The accumulated distribution of quadratic forms on the sphere. Linear Algebra and Its Applications 245, 335-351.
15. Schechter, M. (1998) Integration over a polyhedron: An application of the Fourier-Motzkin elimination method. American Mathematical Monthly 105, 246-251.
16. Tjur, T. (1980) Probability Based on Radon Measures. Wiley Series in Probability and Mathematical Statistics. New York: Wiley.
17. von Neumann, J. (1941) Distribution of the ratio of the mean square successive difference to the variance. Annals of Mathematical Statistics 12, 367-395.