Abstract After coal mining, mining fissures develop, which may lead to an overlying aquifer and water inrush. Objectively accurately evaluating predicting the abundance of bottom Cenozoic are great significance for ensuring safe shallow seams protection resources. The richness evaluation index data has characteristics high dimensionality, nonlinearity, nonnormal distribution, therefore, results...

We study the estimation of linear discriminant with projection pursuit, a method that is unsupervised in sense it does not use class labels estimation. Our viewpoint asymptotic and, as our main contribution, we derive central limit theorems for estimators based on three different indices, skewness, kurtosis, and their convex combination. The results show each case limiting covariance matrix pro...

We derive a rst-order approximation of the density of maximum entropy for a continuous 1-D random variable, given a number of simple constraints. This results in a density expansion which is somewhat similar to the classical polynomial density expansions by Gram-Charlier and Edgeworth. Using this approximation of density, an approximation of 1-D diierential entropy is derived. The approximation...