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1. On the power of Chatterjee’s rank correlation

   https://doi.org/10.1093/biomet/asab028  

   Shi, H; Drton, M; Han, F (October 2021, Biometrika)

   Summary Chatterjee (2021) introduced a simple new rank correlation coefficient that has attracted much attention recently. The coefficient has the unusual appeal that it not only estimates a population quantity first proposed by Dette et al. (2013) that is zero if and only if the underlying pair of random variables is independent, but also is asymptotically normal under independence. This paper compares Chatterjee’s new correlation coefficient with three established rank correlations that also facilitate consistent tests of independence, namely Hoeffding’s $$D$$, Blum–Kiefer–Rosenblatt’s $$R$$, and Bergsma–Dassios–Yanagimoto’s $$\tau^*$$. We compare the computational efficiency of these rank correlation coefficients in light of recent advances, and investigate their power against local rotation and mixture alternatives. Our main results show that Chatterjee’s coefficient is unfortunately rate-suboptimal compared to $$D$$, $$R$$ and $$\tau^*$$. The situation is more subtle for a related earlier estimator of Dette et al. (2013). These results favour $$D$$, $$R$$ and $$\tau^*$$ over Chatterjee’s new correlation coefficient for the purpose of testing independence. 

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2. On boosting the power of Chatterjee’s rank correlation

   https://doi.org/10.1093/biomet/asac048  

   Lin, Z.; Han, F. (August 2022, Biometrika)

   Summary The ingenious approach of Chatterjee (2021) to estimate a measure of dependence first proposed by Dette et al. (2013) based on simple rank statistics has quickly caught attention. This measure of dependence has the appealing property of being between 0 and 1, and being 0 or 1 if and only if the corresponding pair of random variables is independent or one is a measurable function of the other almost surely. However, more recent studies (Cao & Bickel 2020; Shi et al. 2022b) showed that independence tests based on Chatterjee’s rank correlation are unfortunately rate inefficient against various local alternatives and they call for variants. We answer this call by proposing an improvement to Chatterjee’s rank correlation that still consistently estimates the same dependence measure, but provably achieves near-parametric efficiency in testing against Gaussian rotation alternatives. This is possible by incorporating many right nearest neighbours in constructing the correlation coefficients. We thus overcome the ‘ only one disadvantage’ of Chatterjee’s rank correlation (Chatterjee, 2021, § 7). 

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3. On relationships between Chatterjee’s and Spearman’s correlation coefficients

   https://doi.org/10.1080/03610926.2024.2309971  

   Zhang, Qingyang (February 2024, Communications in Statistics - Theory and Methods)

   In his seminal work, Chatterjee (Citation2021) introduced a novel correlation measure that is distribution-free, asymptotically normal, and consistent against all alternatives. In this article, we study the probabilistic relationships between Chatterjee’s correlation and the widely used Spearman’s correlation. We show that, under independence, the two sample-based correlations are asymptotically joint normal and asymptotically independent. Under dependence, the magnitudes of two correlations can be substantially different. We establish some extreme cases featuring large differences between these two correlations. Motivated by these findings, a new independence test is proposed by combining Chatterjee’s and Spearman’s correlations into a maximal strength measure of variable association. Our simulation study and real-data application show the good sensitivity of the new test to different correlation patterns. 

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4. Within-cluster resampling for multilevel models under informative cluster size

   https://doi.org/10.1093/biomet/asz035  

   Lee, D.; Kim, J. K.; Skinner, C. J. (July 2019, Biometrika)

   Summary A within-cluster resampling method is proposed for fitting a multilevel model in the presence of informative cluster size. Our method is based on the idea of removing the information in the cluster sizes by drawing bootstrap samples which contain a fixed number of observations from each cluster. We then estimate the parameters by maximizing an average, over the bootstrap samples, of a suitable composite loglikelihood. The consistency of the proposed estimator is shown and does not require that the correct model for cluster size is specified. We give an estimator of the covariance matrix of the proposed estimator, and a test for the noninformativeness of the cluster sizes. A simulation study shows, as in Neuhaus & McCulloch (2011), that the standard maximum likelihood estimator exhibits little bias for some regression coefficients. However, for those parameters which exhibit nonnegligible bias, the proposed method is successful in correcting for this bias. 

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5. Confidence bands for survival curves from outcome‐dependent stratified samples

   https://doi.org/10.1111/sjos.12700  

   Saegusa, Takumi; Nandori, Peter (September 2024, Scandinavian Journal of Statistics)

   Abstract We consider the construction of confidence bands for survival curves under the outcome‐dependent stratified sampling. A main challenge of this design is that data are a biased dependent sample due to stratification and sampling without replacement. Most literature on regression approximates this design by Bernoulli sampling but variance is generally overestimated. Even with this approximation, the limiting distribution of the inverse probability weighted Kaplan–Meier estimator involves a general Gaussian process, and hence quantiles of its supremum is not analytically available. In this paper, we provide a rigorous asymptotic theory for the weighted Kaplan–Meier estimator accounting for dependence in the sample. We propose the novel hybrid method to both simulate and bootstrap parts of the limiting process to compute confidence bands with asymptotically correct coverage probability. Simulation study indicates that the proposed bands are appropriate for practical use. A Wilms tumor example is presented. 

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