Abstract
If the noises in data are Gaussian and independent, LSQ (least square) estimates of regression parameters are unbiased and of minimum variance. However, if the data are contaminated by outliers, LSQ will result inaccurate estimates of parameters. Robust technic is widely used to avoid the difficulty. The technic requires penalty factors for each data and estimation of parameters is done by LSQ. Specification or selection of penalty function form is left for data analyst. When we adopt distributions which have heavier tails than that of Gaussian, ML (maximum likelihood method) will reduce influences from outliers and will result better estimates of parameters. Once ML estiamtes obtained, AIC (Akaike's Information Criterion) can help us in selecting a proper model of regression from candidates. In this article, Type 7 Pearson system distribution is used as a heavy-tail distribution. The distribution naturaly links Cauchy, approximate Laplace and Gaussian distributions. Consequently the regression procedure with this distribution is robust and has high adaptability to data contaminated by outliers.
