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In order to explore the suitability of a fine-grained classification of journal articles by exploiting multiple sources of information, articles are organized in a two-layer multiplex. The first layer conveys similarities based on the full-text of articles, and the second similarities based on cited references. The information of the two layers are only weakly associated. The Similarity Network Fusion process is adopted to combine the two layers into a new single-layer network. A clustering algorithm is applied to the fused network and the classification of articles is obtained. In order to evaluate its coherence, this classification is compared with the ones obtained by applying the same algorithm to each of two layers. Moreover, the classification obtained for the fused network is also compared with the classifications obtained when the layers of information are integrated using different methods available in literature. In the case of the Cambridge Journal of Economics , Similarity Network Fusion appears to be the best option. Moreover, the achieved classification appears to be fine-grained enough to represent the extreme heterogeneity characterizing the contributions published in the journal.

Polynomial chaos expansion (PCE) has been proven to be a powerful tool for developing surrogate models in the field of uncertainty and global sensitivity analysis. The computational cost of classical PCE is unaffordable since the number of terms grows exponentially with the dimensionality of inputs. This considerably restricts the practical use of PCE. An efficient approach to address this problem is to build a sparse PCE. Since some basis polynomials in representation are highly correlated and the number of available training samples is small, the sparse PCE obtained by the original least square (LS) regression using these samples may not be accurate. Meanwhile, correlation between the non-influential basis polynomial and the important basis polynomials may disturb the correct selection of the important terms. To overcome the influence of correlation in the construction of sparse PCE, a full PCE of model response is first developed based on partial least squares technique in the paper. And an adaptive algorithm based on distance correlation is proposed to select influential basis polynomials, where the distance correlation is used to quantify effectively the impact of basis polynomials on model response. The accuracy of the surrogate model is assessed by leave-one-out cross validation. The proposed method is validated by several examples and global sensitivity analysis is performed. The results show that it maintains a balance between model accuracy and complexity.

In this study, we developed a modified version of the CRiteria Importance Through Inter-criteria Correlation (CRITIC) method, namely the Distance Correlation-based CRITIC (D-CRITIC) method. The usage of the method was illustrated by evaluating the weights of five smartphone criteria. The same evaluation was repeated using four other objective weighting methods, including the original CRITIC method. The results from all the methods were further analyzed based on three different tests (i.e., the distance correlation test, the Spearman rank-order correlation test, and the symmetric mean absolute percentage error test) to validate D-CRITIC. The tests revealed that D-CRITIC could produce more valid criteria weights and ranks than the original CRITIC method since D-CRITIC yielded a higher average distance correlation, a higher average Spearman rank-order correlation, and a lower symmetric mean absolute percentage error. Besides, additional sensitivity analysis indicated that D-CRITIC has the tendency to deliver more stable criteria weights and ranks with a larger decision matrix. The research has contributed an alternative objective weighting method to the area of multi-criteria decision-making through a unique extension of distance correlation. This study is also the first to propose the idea of a distance correlation test to compare the performance of different criteria weighting methods.

Distance covariance and distance correlation are scalar coefficients that characterize independence of random vectors in arbitrary dimension. Properties, extensions and applications of distance correlation have been discussed in the recent literature, but the problem of defining the partial distance correlation has remained an open question of considerable interest. The problem of partial distance correlation is more complex than partial correlation partly because the squared distance covariance is not an inner product in the usual linear space. For the definition of partial distance correlation, we introduce a new Hubert space where the squared distance covariance is the inner product. We define the partial distance correlation statistics with the help of this Hubert space, and develop and implement a test for zero partial distance correlation. Our intermediate results provide an unbiased estimator of squared distance covariance, and a neat solution to the problem of distance correlation for dissimilarities rather than distances.

Distance correlation is a new measure of dependence between random vectors. Distance covariance and distance correlation are analogous to product-moment covariance and correlation, but unlike the classical definition of correlation, distance correlation is zero only if the random vectors are independent. The empirical distance dependence measures are based on certain Euclidean distances between sample elements rather than sample moments, yet have a compact representation analogous to the classical covariance and correlation. Asymptotic properties and applications in testing independence are discussed. Implementation of the test and Monte Carlo results are also presented.

The Pearson correlation coefficient (ρ) is a commonly used measure of correlation, but it has limitations as it only measures the linear relationship between two numerical variables. The distance correlation measures all types of dependencies between random vectors X and Y in arbitrary dimensions, not just the linear ones. In this paper, we propose a filter method that utilizes distance correlation as a criterion for feature selection in Random Forest regression. We conduct extensive simulation studies to evaluate its performance compared to existing methods under various data settings, in terms of the prediction mean squared error. The results show that our proposed method is competitive with existing methods and outperforms all other methods in high-dimensional (p≥300) nonlinearly related data sets. The applicability of the proposed method is also illustrated by two real data applications.

We propose the use of projection correlation to characterize dependence between two random vectors. Projection correlation has several appealing properties. It equals zero if and only if the two random vectors are independent, it is not sensitive to the dimensions of the two random vectors, it is invariant with respect to the group of orthogonal transformations, and its estimation is free of tuning parameters and does not require moment conditions on the random vectors. We show that the sample estimate of the projection correction is n-consistent if the two random vectors are independent and root-n-consistent otherwise. Monte Carlo simulation studies indicate that the projection correlation has higher power than the distance correlation and the ranks of distances in tests of independence, especially when the dimensions are relatively large or the moment conditions required by the distance correlation are violated.

There is a slight gap and error in Remark 3.4 of Ann. Probab. 41, no. 5 (2013), 3284–3305, that was not noticed before the first errata were published (Ann. Probab. 46, no. 4 (2018), 2400–2405). We take this opportunity to provide some additional updates as well.

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.

Distance correlation has become an increasingly popular tool for detecting the nonlinear dependence between a pair of potentially high-dimensional random vectors. Most existing works have explored its asymptotic distributions under the null hypothesis of independence between the two random vectors when only the sample size or the dimensionality diverges. Yet its asymptotic null distribution for the more realistic setting when both sample size and dimensionality diverge in the full range remains largely underdeveloped. In this paper, we fill such a gap and develop central limit theorems and associated rates of convergence for a rescaled test statistic based on the bias-corrected distance correlation in high dimensions under some mild regularity conditions and the null hypothesis. Our new theoretical results reveal an interesting phenomenon of blessing of dimensionality for high-dimensional distance correlation inference in the sense that the accuracy of normal approximation can increase with dimensionality. Moreover, we provide a general theory on the power analysis under the alternative hypothesis of dependence, and further justify the capability of the rescaled distance correlation in capturing the pure nonlinear dependency under moderately high dimensionality for a certain type of alternative hypothesis. The theoretical results and finite-sample performance of the rescaled statistic are illustrated with several simulation examples and a blockchain application.