In a 2004 paper in the Journal of Multivariate Analysis, Carlos A. Coelho laid the foundations for what he called ’near-exact distributions’ (see reference [1] below). Since then these have been successfully applied to a large number of statistics (see references [1]-[24] below). These are distributions which are built using a different philosophy in approximating the exact characteristic function (c.f.) of statistics. The technique combines an adequately developed decomposition of the c.f., most often a factorization, with the action of keeping then most of this c.f. unchanged, and replacing the remaining smaller part by an adequate asymptotic approximation. All this is done in order to obtain a manageable and very well-fitting approximation, which may be used to compute near-exact quantiles or p-values.
The near-exact distributions lie much closer to the exact distribution than common asymptotic distributions and when correctly applied to statistics used in Multivariate Analysis, besides showing an asymptotic behavior for increasing sample sizes, they also show a marked asymptotic behavior for increasing numbers of variables involved.
Besides, these distributions are not too hard to obtain and they are much useful in situations where it is
not possible to obtain the exact distribution in a manageable form. The near-exact distributions may be easily implemented even for tests of highly complicated structures for covariance matrices, by considering the decomposition of the null hypothesis into a set of conditionally independent hypotheses, or by using a technique called ’eigenblock’ and ’eigenmatrix’ decomposition, this later one to be launched soon in a publication.
Very sharp near-exact distributions are available even for statistics for which there are no asymptotic distributions available (see [21] and [22] below).
A page dedicated to the contents of reference [15] below may be found here.
The near-exact distributions lie much closer to the exact distribution than common asymptotic distributions and when correctly applied to statistics used in Multivariate Analysis, besides showing an asymptotic behavior for increasing sample sizes, they also show a marked asymptotic behavior for increasing numbers of variables involved.
Besides, these distributions are not too hard to obtain and they are much useful in situations where it is
not possible to obtain the exact distribution in a manageable form. The near-exact distributions may be easily implemented even for tests of highly complicated structures for covariance matrices, by considering the decomposition of the null hypothesis into a set of conditionally independent hypotheses, or by using a technique called ’eigenblock’ and ’eigenmatrix’ decomposition, this later one to be launched soon in a publication.
Very sharp near-exact distributions are available even for statistics for which there are no asymptotic distributions available (see [21] and [22] below).
A page dedicated to the contents of reference [15] below may be found here.
Meet the team that has been writing the papers below: