Authors
Lanjue Chen, Alan TK Wan, Shuyi Zhang, Yong Zhou
Description
In the following theorem and corollaries, we derive the theoretical properties of the naive estimator θN= K− 1∑ K k= 1 ̂θk n, including the upper bound and the optimal convergence rate of its MSE, and the consistency properties. These results on the naive estimator enable a formal comparison with the properties of our proposed estimators. Theorem S1. Let Conditions (C1)-(C6) be satisfied. In particular, there exists ζ> 0 such that p= O (n 8 τ (1− 1+ ζ 8)) if τ> 0. Then the MSE of the naive estimator is bounded above by the righthand-side of the following inequality:
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