2015/02/11 by Shonosuke Sugasawa, Sugasawa, Shonosuke, Tatsuya Kubokawa +1
Computer Science · Mathematics · #Advanced Statistical Methods and Models #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Methods and Bayesian Inference
paper · pdf · doi:10.48550/arxiv.1502.03193
openalex publication_date 2015/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Box-Cox transformation is applied to the linear mixed models for analyzing positive and grouped data. The problem in using Box Cox transformation is that the maximum likelihood estimator of the transformation parameter is generally inconsistent. To fix it, we suggest a simple and consistent estimator for the transformation parameter based on the moment method. The consistent estimator is used to construct consistent estimators of the parameters involved in the model and under some conditions, the estimators of model parameters are shown to be consistent under m→∞, where m is the number of groups. Moreover, in estimation of the expectation of the (future) observations, it is shown that the resulting estimators also hold consistency owing to the consistent estimator of the transformation parameter. The proposed estimating method is compared with the maximum likelihood method via simulation and it is shown that the proposed estimator works better than the maximum likelihood estimator. Finally, the proposed method is applied to a real data set.