Indeed, in multivariate analysis, most of the commonly used asymptotic distributions worsen their performance when the number of variables increase and even many of them are no longer proper distributions when the number of variables goes above a given threshold. These are facts that have been completely overlooked by other authors and this awkward behavior is not easy to overcome, when we use the common asymptotic techniques. However, by using a dierent approach, which combines an adequate decomposition of the characteristic function of the statistic under study, most often a factorization, with the action of keeping then most of this characteristic function unchanged, and replacing the remaining smaller part by an adequate asymptotic approximation, it is possible to build manageable approximations, called ‘near-exact' approximations, which yield distributions extremely close to the exact distribution, and which exhibit a very good performance for very small sample sizes and an asymptotic behavior not only for increasing sample sizes but also for increasing number of variables involved. These near-exact distributions may then be applied to obtain very well-fitting near-exact quantiles and p-values and they have been, so far, successfully applied to a large number of statistics. Examples are given.
|Title of host publication||Proceedings 59th ISI World Statistics Congress, 25-30 August 2013, Hong Kong|
|Publication status||Published - 1 Jan 2013|
|Event||59th ISI World Statistics Congress - |
Duration: 1 Jan 2013 → …
|Conference||59th ISI World Statistics Congress|
|Period||1/01/13 → …|