1. (Computer Experiment.) Compare the risk of the mle and the James- Stein estimator (12.12) by simulation. Try various values of n and vari- ous vectors θ. Summarize your results.

1. Prove Theorem 13.4.

2. Prove the formulas for the standard errors in Theorem 13.8. You should regard the Xi's as ?xed constants.

3. Consider the regression through the origin model:

Yi = βXi + γ.

Find the least squares estimate for β. Find the standard error of the estimate. Find conditions that guarantee that the estimate is consistent.

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Find the least squares estimate : Find the least squares estimate for β. Find the standard error of the estimate. Find conditions that guarantee that the estimate is consistent. |

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