Christine P. Chai’s contribution to the Discussion of ‘Safe testing’ by Grünwald, De Heide, and Koolen
Christine P. Chai 对《安全检验》的讨论AI 解读 ↓
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Christine P. Chai 对《安全检验》的讨论AI 解读 ↓
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This paper proposes the e-value for ‘safe testing’ as an alternative to the p-value in hypothesis testing. The e-value allows for optional continuation while preserving Type-I error guarantees. I hope to see lots of discussion at the Royal Statistical Society meeting, like the previous ‘Signs and sizes: Understanding and replicating statistical findings’ (Hutton et al., 2020). I have some questions regarding the descriptions: I see some comparisons between the e-value and several alternatives to the ordinary p-value. How does the e-value compare with the sceptical p-value proposed by Held (2020), which is designed to combine replication studies? This paper discusses both optional continuation (OC) and optional stopping (OS) settings. Are there any real-life examples where OC or OS is more appropriate? If we can choose either one, what are the guidelines to decide? In hypothesis testing, β is the probability of making a type II error, i.e. failing to reject the null when it is actually false (Banerjee et al., 2009). I am confused with the narrative, because some parts say the power is set to 1−β=0.8 and other parts say β=0.8. Which is the one used in the experiments? To further improve the manuscript, I also have some comments: It is common to decide whether to perform additional tests depending on the outcome of previous tests, and the rationale is that we do not want to spend money on more testing unless it is necessary. For better clarification, we can state in the motivation that data collection is expensive (Coffey & Elliott, 2024; Jones et al., 2015). I agree with the consensus that we should be cautious in using p-values for hypothesis testing (Wasserstein & Lazar, 2016). There has also been a recent shift from hypothesis testing to estimation as ‘the new statistics’ (Cumming, 2014; Kruschke & Liddell, 2018), and I hope that e-values is a step to better quantification of the decision-making uncertainty. Finally, it is important to make the images accessible to everyone, including people with disabilities. Please make Figures 2 and 4 more readable by increasing the font size of the axis labels. I also recommend using different line shapes to represent each trend, because people with colour blindness may not be able to see the colours. No new data were generated or analysed in support of this research.
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近端估计与推断
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多因子线性资产定价模型 GMM 估计中的效率与定价精度权衡
Even though a multi-factor linear asset pricing model can be equivalently represented in a Beta or in a stochastic discount factor (SDF) form, its inferential efficiency and pricing accuracy features may differ when estimated by the generalized method of moments (GMM), both in small and in large samples. We derive the analytical asymptotic variance of the Beta and the SDF estimators under GMM and find that the SDF approach is likely to be less efficient but to yield more…