General Gaussian estimation (Q1755124)

The paper under review proposes a general Gaussian estimation approach to estimate the parameters in a statistical model. The approach can be used if the joint distribution of the response vector is completely determined by its mean vector and variance-covariance matrix and is identical to the maximum likelihood approach if the response is normal, but not if the response follows other distributions. This approach can provide a closed-form estimation equation once closed-form expressions of the mean vector and variance-covariance matrix of the response vector are available. The paper is organized as follows. In Section 2, the general Gaussian estimation approach is proposed. In Section 3, the author implements the approach to generalized linear mixed effects models. In Section 4, the approach is studied under the framework of longitudinal data. In Section 5, a closed-form estimation approach to the Poisson-lognormal model is presented. Other examples with closed-form estimation functions are provided in Section 6. In Section 7, the author evaluates the performance of the proposed approach under the framework of the Poisson-lognormal model via simulation studies. In Section 8, the approach is applied to a real data example. The paper concludes with a discussion in Section 9.