多維模型的M估計

Abstract

Maronna (1976) 及 Kent 和 Tyler (1996) 都提出多變量具有不變性之M-估計。但是,他們的理論均建構在假設誤差變量具有如下之對稱型分配。 我們提出也具有不變性之M-估計量,但是其理論不需有他們所作之限制 。我們計算出在混合常態分配下之最小平方法及數種M-估計之近似變量數而且也算出C-R下限,用以比較。

Affine equivariant multivariate M-estimators have been proposed by Maronna(1976) and Kent and Tyle(1996). However,their properties were studied under the assumption that random vector follows the spherically symmetric distribution