Indexed on: 07 Oct '14Published on: 07 Oct '14Published in: Natural Resources Research
Ordinary least squares (OLS) regression is an estimation technique widely used in mining research to model relationship among a dependent variable and a set of explanatory variables. However, OLS is based on strong assumption such as normality of the error term, exogeneity of explanatory variables, linearity between regression coefficients, and homoscedasticity. When one or more of the assumption are not held, OLS can lead to biased and inefficient estimates of the true population parameters. Using biased estimates of the population parameters may result in serious problems in mining decision making, especially if key decisions are based on the biased parameter estimates. One of the main reasons that can lead OLS to provide biased estimates is the presence of outlier data points in the sampled population. In this paper, we focus on alternatives to the OLS estimator, which are more robust (or resistant) to the presence of outliers. Two case studies were conducted to compare OLS and robust regression approaches namely L1-estimation, M-estimation, least trimmed squares, least median squares, and MM-estimation. The case studies showed that inference based on OLS in the presence of outliers could lead to bad decisions if regression coefficients are not interpreted correctly. Robust regression approach can provide estimates useful even if a dataset is contaminated with outliers.