In this paper, we propose a nonparametric rank-based alternative to the least-squares independent component analysis algorithm developed. The basic idea is to estimate the squared-loss mutual information, which used as the objective function of the algorithm, based on its copula density version. Therefore, no marginal densities have to be estimated. We provide empirical evaluation of the proposed algorithm through simulation and real data analysis. Since the proposed algorithm uses rank values rather than the actual values of the observations, it is extremely robust to the outliers and suffers less from the presence of noise than the other algorithms.

Determination of the diffusion coefficient on the base of solution of a linear inverse problem of the parameter estimation using the Least-square method is presented in this research. For this propose a set of temperature measurements at a single sensor location inside the heat conducting body was considered. The corresponding direct problem was then solved by the application of the heat fundamental solution.

Pedomodels have become a popular topic in soil science and environmental research. They are predictive functions of certain soil properties based on other easily or cheaply measured properties. The common method for fitting pedomodels is to use classical regression analysis, based on the assumptions of data crispness and deterministic relations among variables. In modeling natural systems such as soil system, in which the above assumptions are not held true, prediction is influential and we must therefore attempt to analyze the behavior and structure of such systems more realistically. In this paper we consider fuzzy least squares regression as a means of fitting pedomodels. The theoretical and practical considerations are illustrated by developing some examples of real pedomodels.