In this article, we introduce new techniques to solve the nonlinear regression problem and the nonlinear classification problem. Our benchmarks suggest that our method for regression is significantly more effective when compared to classical methods and our method for classification is competitive. Our list of classical methods includes least squares, random forests, decision trees, boosted tre...

Small Area estimation is a technique used to estimate parameters of subpopulations with small sample sizes.  Small area estimation is needed  in obtaining information on a small area, such as sub-district or village.  Generally, in some cases, small area estimation uses parametric modeling.  But in fact, a lot of models have no linear relationship between the small area average and the covariat...

A total of 1628 human plasma samples from Cycle 1 of the Canadian Health Measures Survey were assayed for total 25-hydroxyvitamin D using the DiaSorin RIA method and the Diasorin “LIAISON 25 OH Vitamin D Total” method. Bland-Altman comparison showed an average bias of 4.8 ± 16.7 nmol/L (6.3%: P<0.001) with the LIAISON method giving higher values. The relationship was investigated using linear a...

The problem of combining predictors to increase accuracy (often called ensemble learning) has been studied broadly in the machine learning community for both classification and regression tasks. The design of an ensemble is based on the individual accuracy of the predictors and also how different they are from one another. There is a significant body of literature on how to design and measure d...

A novel generalization of linear scale space is presented. The generalization allows for a sparse approximation of the function at a certain scale. To start with, we first consider the Tikhonov regularization viewpoint on scale space theory [15]. The sparsification is then obtained using ideas from support vector machines [22] and based on the link between sparse approximation and support vecto...

To determine the timing of peak bone mass and density, we conducted a cross-sectional study of bone mass measurements in 265 premenopausal Caucasian females, aged 8-50 yr. Bone mass and bone mineral density were measured using dual X-ray absorptiometry and single-photon absorptiometry at the spine (anteroposterior, lateral), proximal femur, radius shaft, distal forearm, and the whole body. Bone...

We study the Laha-Lukacs property of the free Meixner laws (processes). We prove that some families of free Meixner distribution have the linear regression function. We also show that this families have the property of quadratic conditional variances.