Hirose Yuichi, Liu Ivy
School of Mathematics and Statistics, Victoria University of Wellington, P.O. Box 600, 6140 Wellington, New Zealand.
Entropy (Basel). 2020 Feb 28;22(3):278. doi: 10.3390/e22030278.
There is a difficulty in finding an estimate of the standard error (SE) of the profile likelihood estimator in the joint model of longitudinal and survival data. The difficulty is on the differentiation of an implicit function that appear in the profile likelihood estimation. We solve the difficulty by introducing the "statistical generalized derivative". The derivative is used to show the asymptotic normality of the estimator with the SE expressed in terms of the profile likelihood score function.
在纵向数据和生存数据的联合模型中，要找到轮廓似然估计量的标准误差（SE）的估计值存在困难。困难在于轮廓似然估计中出现的隐函数的求导。我们通过引入“统计广义导数”来解决这一困难。该导数用于证明估计量的渐近正态性，其中SE用轮廓似然得分函数表示。
