Μη γραμμικά μοντέλα παλινδρόμησης και εφαρμογές

Abstract

Nonlinear regression is quite similar to linear regression, which has been studied extensively by statisticians for many decades. However, the non-linear model is not so easy to deal with, since the loss of linearity creates several theoretical problems, which must be addressed in different ways than in linear regression. The well-known analysis and geometry of least squares are no longer valid, so it is inevitable to resort to asymptomatic methods and iterative algorithms. A non-linear model has the general form Yi=f(Xi,β)+ei, where Xi is the vector of the predicted variables and β is the vector of the parameters. To date, several key results on nonlinear regression have been developed, as this topic is of particular interest and practical importance with mumerous applications to problems in many scientific areas. In the present Thesis, the general model of nonlinear regression is first described and then a systematic presentation of the model parameter estimation techniques is made. Statistical inference topics are covered and the various methods that exist are compared. Finally, the Thesis presents specific areas where nonlinear regression models have been used.