robust regression method / a comparison study

Abstract: the least squares method (ls) is one of the most common methods for estimating the coefficients of linear regression models. however, it is not robust model against the existence of non-linear data. in this study, classical least squares (cls), least median squares (lms) and spline model (sm) are studied. the cls regression, which consists of minimizing the sum of the squared residuals assumes among others a normal error distribution. the lms method as a median-based robust regression method is based on the minimization of the median of the squared residuals.[1] in sm, splines are function estimates obtained by fitting piecewise polynomials and the x range is split into fixed intervals. the intervals are separated by so-called knot locations [2]. in each interval a polynomial is fit with the constraint that at the knot locations the function be continuous. a spline is defined by its degree, by the number of knot locations, by the position of knots and by the coefficient of polynomial fitted at each interval. cls, lms and sm are among the studied methods that have r-square 0.706, 0.709 and 0.994 in the data generated according to y = exp (√x + e) equation, respectively. graphical abstract shows the predicted values versus reference values by cls, lms and sm methods. it was concluded that the sm algorithm seems to have a better result of data due to the r-square.