A rank-invariant clustering of variables is introduced that is based on the predictive strength between groups of variables, i.e., two groups are assigned a high similarity if the variables in the first group contain high predictive information about the behaviour of the variables in the other group and/or vice versa. The method presented here is model-free, dependence-based and does not require any distributional assumptions. Various general invariance and continuity properties are investigated, with special attention to those that are beneficial for the agglomerative hierarchical clustering procedure. A fully non-parametric estimator is considered whose excellent performance is demonstrated in several simulation studies and by means of real-data examples.

Zero-inflated data naturally appears in many applications, such as health care, weather forecasting, and insurance. Analyzing zero-inflated data is challenging as the high amount of observations in zero invalidates standard statistical techniques. For example, assessing the level of dependence between two zero-inflated random variables becomes difficult due to limitations when applying standard rank-based measures of association, such as Kendall’s tau or Spearman’s rho. Recent work tackles this issue and suggests an estimator of Kendall’s tau for zero-inflated continuous distributions. However, such an estimator does not show satisfactory performances for zero-inflated count data. We fill this gap and propose an adjusted estimator for zero-inflated discrete distributions. We derive the estimator analytically and show that it outperforms existing estimators in various simulated scenarios. Finally, we facilitate the interpretability of the proposed estimator by deriving its achievable bounds.

Kendall's tau and conditional Kendall's tau matrices are multivariate (conditional) dependence measures between the components of a random vector. For large dimensions, available estimators are computationally expensive and can be improved by averaging. Under structural assumptions on the underlying Kendall's tau and conditional Kendall's tau matrices, we introduce new estimators that have a significantly reduced computational cost while keeping a similar error level. In the unconditional setting we assume that, up to reordering, the underlying Kendall's tau matrix is block-structured with constant values in each off-diagonal blocks. The estimators take advantage of this block structure by averaging over (part of) the pairwise estimates in each off-diagonal blocks. Derived explicit variance expressions show their improved efficiency. In the conditional setting, the conditional Kendall's tau matrix is assumed to have a block structure given some covariate. Conditional Kendall's tau matrix estimators are constructed as in the unconditional case by averaging. We establish their joint asymptotic normality, and show that the asymptotic variance is reduced compared to the naive estimators. We perform a simulation study displaying improved performance for all estimators. The estimators are used to compute VaR of a large stock portfolio; backtesting illustrates the obtained improvements compared to the previous estimators.