Accurate bias estimation with applications to focused model selection
推导了偏差和平方偏差的近似公式，误差阶数为样本量的倒数，适用于分位数、无偏估计的变换、最大似然估计等广泛估计量，并基于平方偏差估计提出了新的聚焦信息准则（FIC）用于模型选择。
Abstract We derive approximations to the bias and squared bias with errors of order where is the sample size. Our results hold for a large class of estimators, including quantiles, transformations of unbiased estimators, maximum likelihood estimators in (possibly) incorrectly specified models, and functions thereof. Furthermore, we use the approximations to derive estimators of the mean squared error (MSE) which are correct to order . Since the variance of many estimators is of order , this level of precision is needed for the MSE estimator to properly take the variance into account. We also formulate a new focused information criterion (FIC) for model selection based on the estimators of the squared bias. Lastly, we illustrate the methods on data containing the number of battle deaths in all major inter‐state wars between 1823 and the present day. The application illustrates the potentially large impact of using a less‐accurate estimator of the squared bias.