The Error Performances of Some Residual Optimization Methods

A good statistic is unbiased and efficient. Because the encountered data in practice is a sample data with a certain size, the required statistic is not unbiased statistic, but statistic that has small error. When the encountered data is only a sample data, then that can be done is not error optimization but is residual optimization. This study aims to examine the error performance of three methods of residual optimization, they are by minimizing the maximum of absolute residual (MLAD), by minimizing the sum of absolute residual (LAD), and by minimizing the sum of squared residual (LS). Research results using simulation experiments showed that if the data have uniform distribution, the residual optimization method by minimizing maximum of absolute residual get the smallest error. Meanwhile, residual optimization method by minimizing the sum of squared residual get the smallest error when the data have normal or exponential distribution. This property is true when statistics to be estimated are measure of central tendency, regression coefficients, and the response of regression.