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Choice of Estimators Based on Different Observations: Modified AIC and LCV Criteria

机译:基于不同观察值的估计量选择:修改后的AIC和LCV标准

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It is quite common in epidemiology that we wish to assess the quality of estimators on a particular set of information, whereas the estimators may use a larger set of information. Two examples are studied: the first occurs when we construct a model for an event which happens if a continuous variable is above a certain threshold. We can compare estimators based on the observation of only the event or on the whole continuous variable. The other example is that of predicting the survival based only on survival information or using in addition information on a disease. We develop modified Akaike information criterion (AIC) and Likelihood cross-validation (LCV) criteria to compare estimators in this non-standard situation. We show that a normalized difference of AIC has a bias equal to o{n x) if the estimators are based on well-specified models; a normalized difference of LCV always has a bias equal to o(n~x). A simulation study shows that both criteria work well, although the normalized difference of LCV tends to be better and is more robust. Moreover in the case of well-specified models the difference of risks boils down to the difference of statistical risks which can be rather precisely estimated. For 'compatible' models the difference of risks is often the main term but there can also be a difference of mis-specification risks.
机译:在流行病学中,我们很希望评估一组特定信息的估计量,而这些估计量可能会使用更多的信息。研究了两个示例:第一个示例是当我们为事件构建模型时发生的情况,如果连续变量高于某个阈值,则会发生该事件。我们可以仅根据事件的观察结果或整个连续变量来比较估计量。另一个例子是仅根据生存信息或使用疾病的附加信息来预测生存的例子。我们开发了修改后的Akaike信息标准(AIC)和似然交叉验证(LCV)标准,以比较这种非标准情况下的估计量。我们表明,如果估计量基于明确指定的模型,则AIC的归一化差异的偏差等于o(n x)。 LCV的归一化差始终具有等于o(n〜x)的偏差。仿真研究表明,尽管LCV的标准化差异趋于更好且更稳健,但这两个标准均适用。此外,在模型明确的情况下,风险差异归结为可以相当精确地估计的统计风险差异。对于“兼容”模型,风险差异通常是主要术语,但错误指定风险也可能存在差异。

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