Abstract Statistical analysis of inter-variable relationships in multivariate time series plays a central role in econometrics and engineering. Existing approaches based on vector autoregressive models and spectral decompositions often rely on assumptions that limit their interpretability when innovation variables are correlated. This paper highlights these limitations and proposes a decomposition of the predictive spectral density matrix under a finite prediction horizon. Based on this framework, we introduce the Predictive Relative Power Contribution (PRPC), which generalizes relative power contribution measures to the predictive setting. The practical utility of the proposed approach is illustrated and discussed.

Abstract Correlation tests are very important tools for the pathway analysis or graphical modeling of high-dimensional data. In this study, we consider a correlation test under the strongly spiked eigenvalue (SSE) model in high-dimension, low-sample-size scenarios, where the sample size is much smaller than the dimension. High-dimensional data often fit the SSE model. Previously, a high-dimensional test for a correlation matrix under the non-SSE model was constructed using the extended cross-data-matrix (ECDM) methodology. Here, we show that an asymptotic distribution of the test statistic using ECDM methodology under the SSE model can be written using the distribution of the sum of some weighted chi-squared variables when both dimension and sample size reach infinity. We propose a new test procedure using the asymptotic distribution. We also show that the proposed test procedure has preferable properties for power and size. We discuss the performance of the test procedure through simulations and present a demonstration with actual data analyses using a microarray data set.

An event that hinders or changes the possibility of observing the event of interest is called a competing risk. For instance, clinical studies for those with multimorbidity or critically severe illnesses often require consideration of competing risks, as the occurrence of other events may preclude the primary event of interest. Since the one-to-one correspondence between the cause-specific hazard and the cause-specific incidence is lost in the classical competing risk model (Andersen et al., International Journal of Epidemiology 41:861–870, 2012), the Fine-Gray hazard was developed. The cause-specific incidence and the Fine-Gray hazard have been widely used and have become the default methods in competing risk analysis. The cause-specific incidence, however, often fails to represent treatment effects properly due to failures of the competing causes, particularly when the hazards of the competing causes are considerably different between the control and treatment arms. This study introduces a new incidence termed, cause-distinct incidence, which has a one-to-one correspondence with the cause-specific hazard and is less affected by competing causes than the cause-specific incidence. Whilst, recent studies have found unexpected effects of censors on the Fine-Gray hazard analysis. For instance, the estimation of the censoring distribution can affect the accuracy or censoring can complicate the estimation. The root cause of these unexpected phenomena has been uninvestigated. The basic requirement for the hazard is that it be independent of the distribution of independent censoring. Nevertheless, this study verifies mathematically and also numerically that the Fine-Gray hazard depends on the distribution of independent censoring.

In high dimensional regression, clustering features according to their effects on outcomes is often as important as feature selection. For example, insurance premiums are set for each rate class pertaining to risk factors related to claim risk. To calculate reliable insurance premiums, it is often necessary to group the numerous rate classes into fewer classes. However, the combinations of ways to consolidate rate classes are vast, and it is computationally challenging to consider each combination individually. Under such circumstances, sparse regularization techniques for feature clustering are extremely useful as methods that automatically consolidate rate classes with no significant differences in risk levels during the estimation process. For this purpose, clustered Lasso and octagonal shrinkage and clustering algorithm for regression (OSCAR) can be used to generate feature groups automatically using pairwise L1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L_1$$\\end{document} norm and pairwise L∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L_\\infty $$\\end{document} norm, respectively. This paper proposes efficient path algorithms for clustered Lasso and OSCAR to construct solution paths with respect to their regularization parameters. Despite the excessive terms in exhaustive pairwise regularization, their computational costs are reduced by using the symmetry of those terms. Simple equivalent conditions to check subgradient equations in each feature group are derived using the graph theory. The proposed algorithms are shown to be more efficient than existing algorithms via numerical experiments.