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Bergsma and Dassios (2014) introduced an independence measure which is zero if and only if two random variables are independent. This measure can be naively calculated in $O(n^4)$. Weihs et al. (2015) showed that it can be calculated in $O(n^2 log n)$. In this note we will show that using the methods described in Heller et al. (2016), the measure can easily be calculated in only $O(n^2)$.
In an extension of Kendalls $tau$, Bergsma and Dassios (2014) introduced a covariance measure $tau^*$ for two ordinal random variables that vanishes if and only if the two variables are independent. For a sample of size $n$, a direct computation of $
The prevalence of multivariate space-time data collected from monitoring networks and satellites or generated from numerical models has brought much attention to multivariate spatio-temporal statistical models, where the covariance function plays a k
The consistency and asymptotic normality of the spatial sign covariance matrix with unknown location are shown. Simulations illustrate the different asymptotic behavior when using the mean and the spatial median as location estimator.
In this paper, we consider the Graphical Lasso (GL), a popular optimization problem for learning the sparse representations of high-dimensional datasets, which is well-known to be computationally expensive for large-scale problems. Recently, we have
We introduce an information criterion, PCIC, for predictive evaluation based on quasi-posterior distributions. It is regarded as a natural generalisation of the widely applicable information criterion (WAIC) and can be computed via a single Markov ch