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An approximation to the distribution of quadratic forms in normal random variables. (English) Zbl 0652.62017
Aust. J. Stat. 30A, Spec. Issue, 150-159 (1988).
A new approximation to the distribution of quadratic forms in normal random variables is derived. It is based on the Edgeworth expansion and a bound on the error involved in the approximation is given. The new approximation is compared with others for a particular quadratic form which arises in the estimation of variance in a non-parametric regression.

MSC:
62E20 Asymptotic distribution theory in statistics
62H10 Multivariate distribution of statistics