Direct construction of the probability distribution function for a Poisson binomial random variable, where success probabilities may vary from trial to trial, requires on the order of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$2^{n}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msup> <mn>2</mn> <mi>n</mi> </msup> </math> </EquationSource> </InlineEquation> calculations, and is computationally infeasible for all but modest sized problems. An...</equationsource></equationsource></inlineequation>

In this paper, we address data collinearity problems in multiple linear regression from an optimization perspective. We propose a novel linearly constrained quadratic programming model, based on the concept of the variance inflation factor (VIF). We employ the perturbation method that involves...

In parameter estimation, it is not a good choice to select a “best model” by some criterion when there is model uncertainty. Model averaging is commonly used under this circumstance. In this paper, transformation-based model averaged tail area is proposed to construct confidence interval,...

In medicine and health sciences mixed effects models are often used to study time-structured data. Optimal designs for such studies have been shown useful to improve the precision of the estimators of the parameters. However, optimal designs for such studies are often derived under the...

One of the important aspects of exploratory factor analysis (EFA) is to discover underlying structures in real life problems. Especially, R-mode methods of EFA aim to investigate the relationship between variables. Visualizing an efficient EFA model is as important as obtaining one. A good graph...

Investigations focusing on differences in scale parameters across multiple samples appear in various scientific fields, e.g., when assessing measurement precision. In such cases a natural order of groups often suggests itself, which can be exploited by tests involving ordered alternatives. We...

Simultaneous estimation in nonlinear multivariate regression contexts is a complex problem in inference. In this paper, we compare the methodology suggested in the literature for an unknown covariance matrix among response components, the methodology by Beauchamp and Cornell (B&C), with the...

We analyse some possibilities for constructing an aggregated measure of the development of socio-economical objects in terms of their composite phenomenon (i.e., phenomenon described by many statistical features) if the relevant data are expressed as intervals. Such a measure, based on the...

We consider two Riemannian geometries for the manifold <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${\mathcal{M }(p,m\times n)}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi mathvariant="script">M</mi> <mo stretchy="false">(</mo> <mi>p</mi> <mo>,</mo> <mi>m</mi> <mo>×</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mrow> </math> </EquationSource> </InlineEquation> of all <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$m\times n$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>m</mi> <mo>×</mo> <mi>n</mi> </mrow> </math> </EquationSource> </InlineEquation> matrices of rank <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$p$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>p</mi> </math> </EquationSource> </InlineEquation>. The geometries are induced on <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$${\mathcal{M }(p,m\times n)}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi mathvariant="script">M</mi> <mo stretchy="false">(</mo> <mi>p</mi> <mo>,</mo> <mi>m</mi> <mo>×</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mrow> </math> </EquationSource> </InlineEquation> by viewing it as the base...</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>

We provide a detailed hands-on tutorial for the R add-on package <Emphasis Type="Bold">mboost. The package implements boosting for optimizing general risk functions utilizing component-wise (penalized) least squares estimates as base-learners for fitting various kinds of generalized linear and generalized additive...</emphasis>