Lodhi Chandrakant, Tripathi Yogesh Mani
Department of Mathematics, Indian Institute of Technology Patna, Bihta, India.
J Appl Stat. 2019 Oct 17;47(8):1402-1422. doi: 10.1080/02664763.2019.1679096. eCollection 2020.
In this paper, we consider the problem of making statistical inference for a truncated normal distribution under progressive type I interval censoring. We obtain maximum likelihood estimators of unknown parameters using the expectation-maximization algorithm and in sequel, we also compute corresponding midpoint estimates of parameters. Estimation based on the probability plot method is also considered. Asymptotic confidence intervals of unknown parameters are constructed based on the observed Fisher information matrix. We obtain Bayes estimators of parameters with respect to informative and non-informative prior distributions under squared error and linex loss functions. We compute these estimates using the importance sampling procedure. The highest posterior density intervals of unknown parameters are constructed as well. We present a Monte Carlo simulation study to compare the performance of proposed point and interval estimators. Analysis of a real data set is also performed for illustration purposes. Finally, inspection times and optimal censoring plans based on the expected Fisher information matrix are discussed.
在本文中，我们考虑在渐进I型区间删失下对截断正态分布进行统计推断的问题。我们使用期望最大化算法获得未知参数的最大似然估计，随后，我们还计算了参数的相应中点估计。还考虑了基于概率图方法的估计。基于观测到的费舍尔信息矩阵构建未知参数的渐近置信区间。我们在平方误差和线性指数损失函数下，针对信息性和非信息性先验分布获得参数的贝叶斯估计。我们使用重要性抽样程序计算这些估计。还构建了未知参数的最高后验密度区间。我们进行了蒙特卡罗模拟研究，以比较所提出的点估计和区间估计的性能。为了说明目的，还对一个真实数据集进行了分析。最后，讨论了基于期望费舍尔信息矩阵的检查时间和最优删失计划。
