Estimation in linear models based on observations with unknown and possibly unequal scaling

• 成果类型: Article
• 署名作者: Jensen, Soren Tolver; Madsen, Jesper
• 署名单位: University of Copenhagen; Novo Nordisk
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/016214506000000393
• 发表日期: 2006
• 页码: 1059-1064
• 关键词: coefficients

摘要

We consider k groups of observations X-11...,X(1n)1..,X-kl...,X-knk and unknown scalars lambda l,...,lambda k, and we assume that the distribution of the scaled observations X-11/ lambda(1),...,X-ln1/lambda(1),...,X-k1/lambda X-k,...,(knk)/lambda(k) follows a normal linear model on Rnl+...+nk. This general setup includes several interesting models that have appeared in the literature in different contexts and fields of application. The simplest example is the model of equal coefficients of variation in k normal samples. We give, in the general setup, a necessary and sufficient condition in terms of degrees of freedom for when the maximum likelihood estimator (MLE) exists and is unique with probability 1, and furthermore, we give an algorithm for obtaining the MLE.