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I present the Phase Distance Correlation (PDC) periodogram -- a new periodicity metric, based on the Distance Correlation concept of Gabor Szekely. For each trial period PDC calculates the distance correlation between the data samples and their phases. PDC requires adaptation of the Szekelys distance correlation to circular variables (phases). The resulting periodicity metric is best suited to sparse datasets, and it performs better than other methods for sawtooth-like periodicities. These include Cepheid and RR-Lyrae light curves, as well as radial velocity curves of eccentric spectroscopic binaries. The performance of the PDC periodogram in other contexts is almost as good as that of the Generalized Lomb-Scargle periodogram. The concept of phase distance correlation can be adapted also to astrometric data, and it has the potential to be suitable also for large evenly-spaced datasets, after some algorithmic perfection.
We introduce an improvement to a periodicity metric we have introduced in a previous paper.We improve on the Hoeffding-test periodicity metric, using the Blum-Kiefer-Rosenblatt (BKR) test. Besides a consistent improvement over the Hoeffding-test appr
We introduce and test several novel approaches for periodicity detection in unevenly-spaced sparse datasets. Specifically, we examine five different kinds of periodicity metrics, which are based on non-parametric measures of serial dependence of the
We discuss methods currently in use for determining the significance of peaks in the periodograms of time series. We discuss some general methods for constructing significance tests, false alarm probability functions, and the role played in these by
We investigate the problem of testing whether $d$ random variables, which may or may not be continuous, are jointly (or mutually) independent. Our method builds on ideas of the two variable Hilbert-Schmidt independence criterion (HSIC) but allows for
This paper introduces a new method named Distance-based Independence Screening for Canonical Analysis (DISCA) to reduce dimensions of two random vectors with arbitrary dimensions. The objective of our method is to identify the low dimensional linear