Spline and entropy optimization models and applications

This thesis dissertation describes utilizing basis function in constructing spline functions. Different data set assessment and simulation studies are observed using nonparametric regression techniques, such as B-spline, smoothing spline, penalized spline, additive and generalized additive models in multivariate case. It is shown that some explanatory variables have nonlinear effect in models. In this case penalized splines and smoothing splines showed better results. The optimum selection of smoothing parameter implemented with cross validation and generalized cross validation methods. On the other hand, spline methods used in estimation of cumulative distribution function. Entropy optimization methods are widely used technique in estimation of distribution functions. Random variables that does not fit with known statistical distributions are obtained using Entropy Optimization and Generalized Entropy Optimization methods. Distribution of real data set are obtained using MaxEnt, MinxEnt, and their generalized versions, MinMaxEnt, MaxMaxEnt, MaxMinxEnt distributions. Obtained results are compared with spline functions. It has been written functions and procedures for construction B-spline, smoothing spline, penalized spline in R software. Functions for obtaining MinMaxEnt, MaxMaxEnt, MaxMinxEnt distributions also were constructed in R software.