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1. Testing Mutual Independence in High Dimension via Distance Covariance

   https://doi.org/10.1111/rssb.12259  

   Yao, Shun ; Zhang, Xianyang ; Shao, Xiaofeng ( October 2017 , Journal of the Royal Statistical Society Series B: Statistical Methodology)

   We introduce an L2-type test for testing mutual independence and banded dependence structure for high dimensional data. The test is constructed on the basis of the pairwise distance covariance and it accounts for the non-linear and non-monotone dependences among the data, which cannot be fully captured by the existing tests based on either Pearson correlation or rank correlation. Our test can be conveniently implemented in practice as the limiting null distribution of the test statistic is shown to be standard normal. It exhibits excellent finite sample performance in our simulation studies even when the sample size is small albeit the dimension is high and is shown to identify non-linear dependence in empirical data analysis successfully. On the theory side, asymptotic normality of our test statistic is shown under quite mild moment assumptions and with little restriction on the growth rate of the dimension as a function of sample size. As a demonstration of good power properties for our distance-covariance-based test, we further show that an infeasible version of our test statistic has the rate optimality in the class of Gaussian distributions with equal correlation.

    

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2. Nearly minimax optimal Wasserstein conditional independence testing

   https://doi.org/10.1093/imaiai/iaae033  

   Neykov, Matey ; Wasserman, Larry ; Kim, Ilmun ; Balakrishnan, Sivaraman ( December 2024 , Information and Inference: A Journal of the IMA)

   This paper is concerned with minimax conditional independence testing. In contrast to some previous works on the topic, which use the total variation distance to separate the null from the alternative, here we use the Wasserstein distance. In addition, we impose Wasserstein smoothness conditions that on bounded domains are weaker than the corresponding total variation smoothness imposed, for instance, by Neykov et al. (2021, Ann. Statist., 49, 2151–2177). This added flexibility expands the distributions that are allowed under the null and the alternative to include distributions that may contain point masses for instance. We characterize the optimal rate of the critical radius of testing up to logarithmic factors. Our test statistic that nearly achieves the optimal critical radius is novel, and can be thought of as a weighted multi-resolution version of the $U$-statistic studied by Neykov et al. (2021, Ann. Statist., 49, 2151–2177).

    

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3. Toward extracting $$\gamma $$ from $$B\rightarrow DK$$ without binning

   https://doi.org/10.1140/epjc/s10052-023-12057-x  

   Backus, Jeffrey V. ; Freytsis, Marat ; Grossman, Yuval ; Schacht, Stefan ; Zupan, Jure ( September 2023 , The European Physical Journal C)

   $$B^\pm \rightarrow DK^\pm $$$B^{\pm }\to D{K}^{\pm }$transitions are known to provide theoretically clean information about the CKM angle$$\gamma $$$\gamma$, with the most precise available methods exploiting the cascade decay of the neutralDintoCPself-conjugate states. Such analyses currently require binning in theDdecay Dalitz plot, while a recently proposed method replaces this binning with the truncation of a Fourier series expansion. In this paper, we present a proof of principle of a novel alternative to these two methods, in which no approximations at the level of the data representation are required. In particular, our new strategy makes no assumptions about the amplitude and strong phase variation over the Dalitz plot. This comes at the cost of a degree of ambiguity in the choice of test statistic quantifying the compatibility of the data with a given value of$$\gamma $$$\gamma$, with improved choices of test statistic yielding higher sensitivity. While our current proof-of-principle implementation does not demonstrate optimal sensitivity to$$\gamma $$$\gamma$, its conceptually novel approach opens the door to new strategies for$$\gamma $$$\gamma$extraction. More studies are required to see if these can be competitive with the existing methods.

    

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4. Testing homogeneity: the trouble with sparse functional data

   https://doi.org/10.1093/jrsssb/qkad021  

   Zhu, Changbo ; Wang, Jane-Ling ( April 2023 , Journal of the Royal Statistical Society Series B: Statistical Methodology)

   Testing the homogeneity between two samples of functional data is an important task. While this is feasible for intensely measured functional data, we explain why it is challenging for sparsely measured functional data and show what can be done for such data. In particular, we show that testing the marginal homogeneity based on point-wise distributions is feasible under some mild constraints and propose a new two-sample statistic that works well with both intensively and sparsely measured functional data. The proposed test statistic is formulated upon energy distance, and the convergence rate of the test statistic to its population version is derived along with the consistency of the associated permutation test. The aptness of our method is demonstrated on both synthetic and real data sets.

    

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5. Orthogonal Samples for Estimators in Time Series

   https://doi.org/10.1111/jtsa.12269  

   Rao, Suhasini_Subba ( November 2017 , Journal of Time Series Analysis)

   Inference for statistics of a stationary time series often involves nuisance parameters and sampling distributions that are difficult to estimate. In this paper, we propose the method of orthogonal samples, which can be used to address some of these issues. For a broad class of statistics, an orthogonal sample is constructed through a slight modification of the original statistic such that it shares similar distributional properties as the centralized statistic of interest. We use the orthogonal sample to estimate nuisance parameters of the weighted average periodogram estimators andL₂‐type spectral statistics. Further, the orthogonal sample is utilized to estimate the finite sampling distribution of various test statistics under the null hypothesis. The proposed method is simple and computationally fast to implement. The viability of the method is illustrated with various simulations.

    

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