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AN APPROXIMATION TO THE DISTRIBUTION OF QUADRATIC FORMS IN NORMAL RANDOM VARIABLES
Author(s) -
Buckley M.J.,
Eagleson G.K.
Publication year - 1988
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1988.tb00471.x
Subject(s) - quadratic equation , mathematics , variance (accounting) , distribution (mathematics) , random variable , parametric statistics , approximation error , normal distribution , quadratic form (statistics) , statistics , mathematical analysis , geometry , accounting , business
summary 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.