This article investigates some unfamiliar properties of the Pearson product-moment correlation coefficient for the estimation of simple correlation coefficient. Although Pearson's r is biased, except for limited situations, and the minimum variance unbiased estimator has been proposed in the literature, researchers routinely employ the sample correlation coefficient in their practical applicati...

A simple consistent nonparametric estimator of the long-run correlation between two series is proposed, based on the estimation of the bivariate k-lag difference correlation. It is shown that the estimator is asymptotically equivalent to the Bartlett kernel spectral estimator of the complex coherency at frequency zero. The asymptotic distribution is derived, with a test for the absence of long-...

The lattice structure of bounded Coulomb systems is explored using a simple zero-temperature slab model. For slabs above a certain size in6nite-volume behavior (i.e., a bcc lattice) occurs. Below this size surface e6'ects dominate and the lattice type depends on the size, usually taking on an fcclike symmetry. This state is similar to the lattice observed in recent computer simulations. These r...

Since the world is full of indeterminacy, the neutrosophics found their place into contemporary research. The fundamental concepts of neutrosophic set, introduced by Smarandache in [7, 8]. Recently, Salama et al. in [14, 15, 16, 32 ], introduced the concept of correlation coefficient of neutrosophic data. In this paper, we introduce and study the concepts of correlation and correlation coeffici...