A note on the C_P statistic under the nested error regression model

Nested error regression models are frequently used in small-area estimation and related problems. Standard regression model selection criterion, when applied to nested error regression models, may result in inefficient model selection methods. We illustrate this point by examining the performance of the C_P statistic through a Monte Carlo simulation study. The inefficiency of the C_P statistic may, however, be rectified by a suitable transformation of the data.