The purpose of this letter is to introduce a modified version the Gerber statistic resulting in enhancement its function as measure statistical co-movement. modification centres around redefinition zones and thresholds, alongside use finite real-valued contributions rather than discrete binary counts assigning value individual co-movements. Arguments for former are based on alignment data serie...

In this note we establish the existence of the first two moments of the asymptotic trace statistic, which appears as weak limit of the likelihood ratio statistic for testing the cointegration rank in a vector autoregressive model and whose moments may be used to develop panel cointegration tests. Moreover, we justify the common practice to approximate these moments by simulating a certain stati...

In the case of two signals with independent pairs of observations (xn; yn) a statistic to estimate the variance of the mutual information estimator has been derived earlier. We present such a statistic for dependent pairs. To derive this statistic it is necessary to avail of a reliable statistic to estimate the variance of the sample mean in case of dependent observations. We derive and discuss...

We express some criticism about the definition of an algorithmic sufficient statistic and, in particular, of an algorithmic minimal sufficient statistic. We propose another definition, which might have better properties.

Inspired by the k-inversion statistic for LLT polynomials, we define a k-inversion number and k-descent set for words. Using these, we define a new statistic on words, called the k-major index, that interpolates between the major index and inversion number. We give a bijective proof that the k-major index is equi-distributed with the major index, generalizing a classical result of Foata and red...