Asymptotic distribution of the reduced rank regression estimator under general conditions

• 成果类型: Article
• 署名作者: Anderson, TW
• 署名单位: Stanford University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1999
• 页码: 1141-1154
• 关键词: MULTIPLE TIME-SERIES; models

摘要

In the regression model Y = eta + BX + Z with Z unobserved, EZ = 0 and EZZ' = Sigma(ZZ), the least squares estimator of B is (B) over cap = SYXSXX-1. If the rank of B is known to be k less than the dimensions of Y and X, the reduced rank regression estimator of B, say (B) over cap(k), depends on the first k canonical variates of Y and X. The asymptotic distribution of (B) over cap(k) is obtained and compared with the asymptotic distribution of (B) over cap(k). The advantage of (B) over cap(k) is characterized.