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小区域估计的实用度量：非对称均方预测误差AI 解读

The mean squared prediction error (MSPE) is widely used in small area estimation (SAE), as well as in other fields of statistics. Despite its popularity, the MSPE is not always practical in that it treats positive error, or over-prediction, and negative error, or under-prediction, equally. In practice, however, the consequences of these two types of errors are often different. This problem has long been known in statistics; however, a practical solution has not received much…

基于类别匹配的混合模型预测AI 解读

Many practical problems are related to prediction, where the main interest is at subject (e.g., personalized medicine) or (small) sub-population (e.g., small community) level. In such cases, it is possible to make substantial gains in prediction accuracy by identifying a class that a new subject belongs to. This way, the new subject is potentially associated with a random effect corresponding to the same class in the training data, so that method of mixed model prediction…

E-MS 算法：不完整数据下的模型选择AI 解读

We propose a procedure associated with the idea of the E-M algorithm for model selection in the presence of missing data. The idea extends the concept of parameters to include both the model and the parameters under the model, and thus allows the model to be part of the E-M iterations. We develop the procedure, known as the E-MS algorithm, under the assumption that the class of candidate models is finite. Some special cases of the procedure are considered, including E-MS…

最佳预测小域估计AI 解读

We derive the best predictive estimator (BPE) of the fixed parameters under two well-known small area models, the Fay–Herriot model and the nested-error regression model. This leads to a new prediction procedure, called observed best prediction (OBP), which is different from the empirical best linear unbiased prediction (EBLUP). We show that BPE is more reasonable than the traditional estimators derived from estimation considerations, such as maximum likelihood (ML) and…

混合模型选择的围栏方法AI 解读

Many model search strategies involve trading off model fit with model complexity in a penalized goodness of fit measure. Asymptotic properties for these types of procedures in settings like linear regression and ARMA time series have been studied, but these do not naturally extend to nonstandard situations such as mixed effects models, where simple definition of the sample size is not meaningful. This paper introduces a new class of strategies, known as fence methods, for…