A robust adjustment of the profile likelihood
剖面似然的稳健调整AI 解读 ↓
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剖面似然的稳健调整
- 研究问题
- 模型轻度误设导致常规方差估计不一致时，如何调整剖面似然获得稳健检验，并评估模型正确时使用该调整的效率代价？
- 方法与思路
- 作者通过方差修正使调整后的剖面似然满足Bartlett第二恒等式，推导稳健统计量的累积量展开和渐近相对效率表达。
- 材料陈述的贡献
- 摘要称调整可产生稳健的有符号根、Wald和得分统计量；模型正确时，偏差与偏度受影响不大，但效率损失可能显著。
- 阅读关注点
- 应核对轻度误设的含义、方差修正的构造、模型正确条件下的展开阶数，以及效率损失结论对应的具体例子。
- 阅读边界
- 依据OpenAlex索引摘要，稿件版本未注明；摘要未给出效率损失数值或完整条件，不能将其推广为稳健方差估计普遍不宜使用。
原文摘要
Under mild misspecifications of model assumptions, maximum likelihood estimates often remain consistent and asymptotically normal. Asymptotic normality will often hold for the signed root of the likelihood ratio statistic and the score statistic as well. However, standard estimates of asymptotic variance are usually inconsistent. This occurs when Bartlett's second identity fails. In the manner of McCullagh and Tibshirani, a variance correction may be used to adjust the profile likelihood so this identity obtains. The resulting likelihood yields the robust versions of the signed root, Wald and score statistic suggested by Kent and Royall. Assuming model correctness, asymptotic expansions for the first three cumulants of each robust statistic are derived. It is seen that bias and skewness are not severely affected by using a robust statistic. An invariant expression derived for the asymptotic relative efficiency of a robust method allows assessment in numerous examples considered. Even for moderately large sample sizes, losses in efficiency are significant, making the misuse of a robust variance estimate potentially costly. Computer algebra is used in many of the calculations reported in this paper.