A new approach to maximum likelihood estimation of sum‐constrained linear models in case of undersized samples
A new approach to maximum likelihood estimation of sum‐constrained linear models in case of undersized samples
复制标题
样本尺寸过小的情况下和约束线性模型最大似然估计的新方法
DOI：
10.1111/1467-9574.00038
复制
发表时间：
1997
影响因子：
1.5
通讯作者：
R. Harkema
中科院分区：
文献类型：
--
作者：
P. M. C. De Boer;R. Harkema
当类别数量 (n) 与观测数量 (T) 相比较大时，用于估计总和约束模型（如需求系统、品牌选择模型等）的最大似然程序会崩溃或产生非常不稳定的估计。在应用研究中，通常通过假设除比例常数之外已知的因变量的同期协方差矩阵来解决此问题。在本文中，我们为具有大量类别的总和约束模型开发了最大似然程序，该程序不需要太多观察，但仍然允许自由估计 n 个协方差参数。
Maximum likelihood procedures for estimating sum‐constrained models like demand systems, brand choice models and so on, break down or produce very unstable estimates when the number of categories (n) is large as compared with the number of observations (T). In applied research, this problem is usually resolved by postulating the contemporaneous covariance matrix of the dependent variables to be known apart from a constant of proportionality. In this paper we develop a maximum likelihood procedure for sum‐constrained models with large numbers of categories, which does not require too many observations, but nevertheless allows for n covariance parameters to be estimated freely.