we obtain sufficient conditions for the series σanλn to be absolutely summable of order k by atriangular matrix.

Let G be a distribution function on Iw’+’ such that the (k + 1)th marginal is lattice. Let 2, denote the sampe mean of n independent observations from G. For s > 3, the s-term Edgeworth expansions are obtained for a wide class of statistics which are smooth functions of 2,. The result is then applied to a statistic similar to the Student’s t-statistic, where the scaling factor, the sample stand...

The absolute configuration of the title compound, C(14)H(13)NO(2)S, was assigned from the synthesis and confirmed by the structure determination. The central six-membered ring of the indolizine system adopts an envelope conformation, the greatest deviation from the mean plane of the ring being 0.459 (2) Å for the N atom. The benzothieno system is planar [mean deviation = 0.009 (2) Å]. In the cr...

Commonly used sums-of-squares-based error or deviation statisticsdlike the standard deviation, the standard error, the coefficient of variation, and the root-mean-square errordoften are misleading indicators of average error or variability. Sums-of-squares-based statistics are functions of at least two dissimilar patterns that occur within data. Both the mean of a set of error or deviation magn...

A novel semi-supervised learning approach based on statistical physics is proposed in this paper. We treat each data point as an Ising spin and the interaction between pairwise spins is captured by the similarity between the pairwise points. The labels of the data points are treated as the directions of the corresponding spins. In semi-supervised setting, some of the spins have fixed directions...

Many risk measures have been recently introduced which (for discrete random variables) result in Linear Programs (LP). While some LP computable risk measures may be viewed as approximations to the variance (e.g., the mean absolute deviation or the Gini’s mean absolute difference), shortfall or quantile risk measures are recently gaining more popularity in various financial applications. In this...