More Like this

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. 

   more » « less
2. When Choices Are Mistakes

   https://doi.org/10.1257/aer.20201550  

   Nielsen, Kirby; Rehbeck, John (July 2022, American Economic Review)

   Using a laboratory experiment, we identify whether decision-makers consider it a mistake to violate canonical choice axioms. To do this, we incentivize subjects to report axioms they want their decisions to satisfy. Then, subjects make lottery choices which might conflict with their axiom preferences. In instances of conflict, we give subjects the opportunity to re-evaluate their decisions. We find that many individuals want to follow canonical axioms and revise their choices to be consistent with the axioms. In a shorter online experiment, we show correlations of mistakes with response times and measures of cognition. (JEL C91, D12, D44, D91) 

   more » « less
3. Quantum coherence, discord and correlation measures based on Tsallis relative entropy

   https://doi.org/10.26421/QIC20.7-8-2  

   Vershynina, Anna (June 2020, Quantum Information and Computation)

   Several ways have been proposed in the literature to define a coherence measure based on Tsallis relative entropy. One of them is defined as a distance between a state and a set of incoherent states with Tsallis relative entropy taken as a distance measure. Unfortunately, this measure does not satisfy the required strong monotonicity, but a modification of this coherence has been proposed that does. We introduce three new Tsallis coherence measures coming from a more general definition that also satisfy the strong monotonicity, and compare all five definitions between each other. Using three coherence measures that we discuss, one can also define a discord. Two of these have been used in the literature, and another one is new. We also discuss two correlation measures based on Tsallis relative entropy. We provide explicit expressions for all three discord and two correlation measure on pure states. Lastly, we provide tight upper and lower bounds on two discord and correlations measures on any quantum state, with the condition for equality. 

   more » « less
4. Significance testing for canonical correlation analysis in high dimensions

   https://doi.org/10.1093/biomet/asab059  

   McKeague, Ian W; Zhang, Xin (November 2021, Biometrika)

   Summary We consider the problem of testing for the presence of linear relationships between large sets of random variables based on a postselection inference approach to canonical correlation analysis. The challenge is to adjust for the selection of subsets of variables having linear combinations with maximal sample correlation. To this end, we construct a stabilized one-step estimator of the Euclidean norm of the canonical correlations maximized over subsets of variables of prespecified cardinality. This estimator is shown to be consistent for its target parameter and asymptotically normal, provided the dimensions of the variables do not grow too quickly with sample size. We also develop a greedy search algorithm to accurately compute the estimator, leading to a computationally tractable omnibus test for the global null hypothesis that there are no linear relationships between any subsets of variables having the prespecified cardinality. We further develop a confidence interval that takes the variable selection into account. 

   more » « less
5. Time-varying correlation structure estimation and local-feature detection for spatio-temporal data

   Zheng, X.; Xue, L.; Qu, A. (October 2018, Journal of Multivariate Analysis)

   Spatial–temporal data arise frequently in biomedical, environmental, political and social science studies. Capturing dynamic changes of time-varying correlation structure is scientifically important in spatio-temporal data analysis. We approximate the time-varying empirical estimator of the spatial correlation matrix by groups of selected basis matrices representing substructures of the correlation matrix. After projecting the correlation structure matrix onto a space spanned by basis matrices, we also incorporate varying-coefficient model selection and estimation for signals associated with relevant basis matrices. The unique feature of the proposed method is that signals at local regions corresponding with time can be identified through the proposed penalized objective function. Theoretically, we show model selection consistency and the oracle property in detecting local signals for the varying-coefficient estimators. The proposed method is illustrated through simulation studies and brain fMRI data. 

   more » « less