多変量線形モデルにおける高次元漸近理論

Abstract

When a statistic with a complicated distribution is dealt, the asymptotic distribution is often used. Even if the exact distribution is complicated, the asymptotic distribution generally becomes simple form such as normal distribution and chi square distribution. There are also previous studies which derive the asymptotic correction due to improve the approximation. However it is empirically known that the classical asymptotic approximations become worse as the dimension becomes large. So we derive some high-dimensional asymptotic results for the multivariate linear model. These results have better approximations in spite of the size of dimension. These results not only derive better approximation but also clarify asymptotic properties of some test statistics.