A Comparison of OLS and Robust Regression Using S-PLUS

arametric statistics use a sample statistic as an estimate of the population parameter; hence a researcher is making an inference about the value of the population parameter given knowledge of a sample statistic. An estimate (estimator) is therefore a value of a sample statistic that provides information about the population parameter. When conducting parametric statistical tests the researcher should be concerned with the properties of estimators (Glass & Hopkins, 1984). The properties of an estimate are important because one wants the sample statistic to be an accurate and stable estimate of the population parameter. The properties of estimators are unbiased, consistent, efficient, and sufficient. An estimate is unbiased when the mean of the sampling distribution of the statistic equals the population parameter being estimated. An estimate is consistent if the sample statistic gets closer to the population parameter as sample size increases. An estimate is efficient if it doesn’t vary much from sample to sample (variance error or sampling error); hence it refers to the precision of estimation. The variance error of the statistic is the variance of the sampling distribution of the statistic. An estimate is sufficient when no other sample statistic is a better estimate of the population parameter. Another concern is how aspects of the data can affect the sample statistic as an estimate of the population parameter. For example, the Pearson correlation coefficient is attenuated when computed with (1) missing data, (2) a restricted range of scores, (3) non-interval level data, or (4) non-normal data. This concern is magnified in the field of parametric statistics when a researcher discovers that the Pearson correlation coefficient is used in numerous multi-variable methods (i.e. multiple regression, path analysis, factor analysis, canonical correlation, and discriminant analysis) to name a few.