Algorithms and complexity for least median of squares regression

Least Median of Squares Regression

Classical least squares regression consists of minimizing the sum of the squared residuals. Many authors have produced more robust versions of this estimator by replacing the square by something else, such as the absolute value. In this article a different approach is introduced in which the sum is replaced by the median of the squared residuals. The resulting estimator can resist the effect of...

Robust PLS regression based on simple least median squares regression

An analysis of the Least Median of Squares regression problem

The optimization problem that arises out of the least median of squared residuals method in linear regression is analyzed. To simplify the analysis, the problem is replaced by an equivalent one of minimizing the median of absolute residuals. A useful representation of the last problem is given to examine properties of the objective function and estimate the number of its local minima. It is sho...

Stochastic Optimization Algorithm Applied to Least Median of Squares Regression

The paper presents a stochastic optimization algorithm for computing of least median of squares regression (LMS) introduced by (Rousseeuw and Leroy 1986). As the exact solution is hard to obtain a random approximation is proposed, which is much cheaper in time and easy to program. A MATLAB program is included.

PEDOMODELS FITTING WITH FUZZY LEAST SQUARES REGRESSION

Pedomodels have become a popular topic in soil science and environmentalresearch. They are predictive functions of certain soil properties based on other easily orcheaply measured properties. The common method for fitting pedomodels is to use classicalregression analysis, based on the assumptions of data crispness and deterministic relationsamong variables. In modeling natural systems such as s...