Comparison and Selection between Biased Estimator and LS Estimator

The problem of selection between biased estimator and LS estimator in GaussMarkov model is studied by using the hypothesis testing approach. Firstly, the comparisons between the two most important biased estimators, ordinary ridge estimator and principal components estimator, and LS estimator are conducted by using the criterion of mean squared error; and the conditions to show the superiority of each of these two estimators over the LS estimator have been obtained. Then, the tests have been suggested to verify whether or not these conditions hold in given situations by using the statistical method. Finally, the computational results demonstrate that if the null hypothesis is accepted with a significance level, we have to believe the reasonability of biased estimator instead of LS estimator and we can think if we use the biased estimator it will improve LS estimator more effectively. On the contrary, if the null hypothesis is rejected, we will suspect the biased estimator's superiority. In this case, using the LS estimator is still a good way. 