Heather Battey's Contribution to the Discussion of 'Assumption-Lean Inference for Generalised Linear Model Parameters' by Vansteelandt and Dukes
Heather Battey's Contribution to the Discussion of 'Assumption-Lean Inference for Generalised Linear Model Parameters' by Vansteelandt and Dukes
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Heather Battey 对 Vansteelandt 和 Dukes 的“广义线性模型参数的假设精益推理”讨论的贡献
DOI：
10.1111/rssb.12517
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发表时间：
2022
影响因子：
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通讯作者：
Battey H
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文献类型：
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作者：
Battey H
对于潜在概率模型存在不确定性的情况，至少有三种广泛的方法。一个是寻求可靠的推理的利益参数，或者也许，正如作者所主张的，数量保留至少在一定程度上的可解释性下的错误说明。另一个是更明确地承认模型的不确定性。第三种方法，松散地连接到第一个，是封装在一个可能的大量的滋扰参数的模型的不确定性，在分析中消除适当的条件参数或其他特定问题的机动（如巴特利特，1937年）。一个有用的例子是使用部分似然来规避比例风险模型的基线风险函数（无限维滋扰参数）。这三种方法的适当性在很大程度上取决于具体情况。如果对一个兴趣参数的解释在模型上是稳定的，那么似乎只有当兴趣参数是正交的（在Jeffreys，1948，pp. 158-184）的名义滋扰参数，其
For situations in which there is uncertainty over the underlying probabilistic model, there are at least three broad approaches. One is to seek reliable inference for interest parameters or perhaps, as the authors advocate, for quantities retaining at least a degree of interpretability under misspecification. Another is to acknowledge more explicitly the model uncertainty. A third approach, loosely connected to the first, is to encapsulate uncertainty over the model in a possibly large number of nuisance parameters, to be eliminated in the analysis by suitable conditioning arguments or other problem-specific manoeuvres (eg Bartlett, 1937). A helpful example is the use of partial likelihood to evade the baseline hazard function (an infinitedimensional nuisance parameter) of a proportional hazards model. The appropriateness of each of the three approaches depends largely on context. I will constrain my discussion to the first two.If the interpretation of an interest parameter is stable over models, it appears that first-order reliable inference via maximum likelihood estimation is possible in spite of considerable misspecification in the nuisance part of the model only when the interest parameter is orthogonal (in the sense of Jeffreys, 1948, pp. 158–184) to the notional nuisance parameters, whose