Semiparametric Estimation of Gamma Processes for Deteriorating Products

This article investigates the semiparametric inference of the simple Gamma-process model and a random-effects variant. Maximum likelihood estimates of the parameters are obtained through the EM algorithm. The bootstrap is used to construct confidence intervals. A simulation study reveals that an estimation based on the full likelihood method is more efficient than the pseudo likelihood method. In addition, a score test is developed to examine the existence of random effects under the semiparametric scenario. A comparison study using a fatigue-crack growth dataset shows that performance of a semiparametric estimation is comparable to the parametric counterpart. This article has supplementary material online.本文针对简易Gamma过程模型（Gamma-process model）及其随机效应变体展开半参数推断研究。通过期望最大化（Expectation-Maximization，EM）算法获得参数的极大似然估计值，并采用Bootstrap方法（Bootstrap）构建置信区间。仿真实验结果表明，基于全似然法的估计相较于伪似然法具有更高的效率。此外，本文构建了得分检验，用于在半参数框架下检验随机效应的存在性。采用疲劳裂纹扩展数据集开展的对比研究显示，半参数估计的性能与参数估计方法相当。本文配有在线补充材料。