Least trimmed squares regression, least median squares regression, and mathematical programming

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...

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...

Robust PLS regression based on simple least median squares regression

Least Squares Percentage Regression

Percentage error (relative to the observed value) is often felt to be more meaningful than the absolute error in isolation. The mean absolute percentage error (MAPE) is widely used in forecasting as a basis of comparison, and regression models can be fitted which minimize this criterion. Unfortunately, no formula exists for the coefficients, and models for a given data set may not be unique. We...

Compressed Least-Squares Regression

We consider the problem of learning, from K data, a regression function in a linear space of high dimensionN using projections onto a random subspace of lower dimension M . From any algorithm minimizing the (possibly penalized) empirical risk, we provide bounds on the excess risk of the estimate computed in the projected subspace (compressed domain) in terms of the excess risk of the estimate b...