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Christian Hennig对《安全检验》的讨论AI 解读

I appreciate the elegance of the theory regarding (RE)GRO(W) e-variables with optional continuation for combining evidence. Here are some rather problematic aspects. (1) The authors state that ‘there seems to be growing consensus that, in the context of hypothesis testing, p-values should either not be used at all, or at least, with utter care’. I see little consensus that p-values should not be used at all. The request for ‘utter care’ is sensible, but I do not believe that…

Hennig 对《广义线性模型参数的弱假设推断》的讨论AI 解读

There is a tendency in statistics to talk about model assumptions in a misleading way. Most of us probably agree with George Box's ‘all models are wrong but some are useful’, yet there is much communication that implies that for applying methods ‘assuming’ certain models, these models have to be true. If this were so, no model-based method could ever be used! Generally model assumptions do not have to be fulfilled. A model assumption just means that certain theoretical…

稳健非正规极大似然：调优、计算及与其他稳健高斯聚类方法的比较AI 解读

The two main topics of this article are the introduction of the “optimally tuned robust improper maximum likelihood estimator” (OTRIMLE) for robust clustering based on the multivariate Gaussian model for clusters, and a comprehensive simulation study comparing the OTRIMLE to maximum likelihood in Gaussian mixtures with and without noise component, mixtures of t-distributions, and the TCLUST approach for trimmed clustering. The OTRIMLE uses an improper constant density for…

位置—尺度混合模型极大似然估计的崩溃点AI 解读

ML-estimation based on mixtures of Normal distributions is a widely used tool for cluster analysis. However, a single outlier can make the parameter estimation of at least one of the mixture components break down. Among others, the estimation of mixtures of t-distributions by McLachlan and Peel [Finite Mixture Models (2000) Wiley, New York] and the addition of a further mixture component accounting for “noise” by Fraley and Raftery [The Computer J. 41 (1998) 578–588] were…