| The purposes of this study are manifold. First, several procedures for the estimation of parameters in linear models are reviewed, including least squares and several non-parametric and robust procedures. The geometric similarities of these differing estimation procedures are reviewed in the context of norms. Corresponding testing procedures for sub-hypotheses are also reviewed and related.; A simulation study was conducted, and the performance of the various procedures was assessed in terms of Type I error rate and statistical power. Monte Carlo simulations included a variety of conditions. Experimental factors in the design of the study included the statistical model, sample size, effect size, and the type of distribution. Both descriptive and inferential statistics were utilized in the analysis of the results from the Monte Carlo simulation.; Both the Serlin and Harwell chi2 test and the R-estimation Score F test maintained nominal Type I error rates quite well across the various distributions and models. The F test had sporadic behavior with the heavy tailed data, though otherwise performed well. The Score test appeared to have the best control of Type I error rates compared to the likelihood ratio and Wald tests. With the power studies, the F test was the most power under normal data conditions, while the quantile procedures had the greatest power for the heavy tailed distributions. The robust alternatives led to substantial increases in power over the F test for the skewed and kurtotic distributions. After adjustment, there appears to be some evidence that the likelihood ratio procedures may be most powerful, though any gain was not great. |
