Weak -consistency of the least weighted squares under heteroscedasticity
Weak nonlinearity in a model which arises from the Helmert transformation
Nowadays, the algorithm most frequently used for determination of the estimators of parameters which define a transformation between two coordinate systems (in this case the Helmert transformation) is derived under one unreal assumption of errorless measurement in the first system. As it is practically impossible to ensure errorless measurements, we can hardly believe that the results of this algorithm are “optimal”. In 1998, Kubáček and Kubáčková proposed an algorithm which takes errors in both...
Weakly nonlinear constraints in regression models
Weakly nonlinear regression model with constraints I: nonlinear hypothesis
The problem considered is under which conditions in weakly nonlinear regression model with constraints I a weakly nonlinear hypothesis can be tested by linear methods. The aim of the paper is to find a region around the approximate value of the regression parameter with the following property. If we are certain that the actual value of the regression parameter is in this region, then the linear method of testing can be used without any significant deterioration of the inference.
Weighted Elastic Net Model for Mass Spectrometry Imaging Processing
In proteomics study, Imaging Mass Spectrometry (IMS) is an emerging and very promising new technique for protein analysis from intact biological tissues. Though it has shown great potential and is very promising for rapid mapping of protein localization and the detection of sizeable differences in protein expression, challenges remain in data processing due to the difficulty of high dimensionality and the fact that the number of input variables in...
When Product Type Experimental Design is Optimal? Brief Survey and New Results.