How do we use Jensen's inequality to prove that $\operatorname E(T_2-\theta)^2 < \operatorname E(T_1-\theta)^2$, where $\theta$ is an unknown constant, $T_1$ is an estimator for $\theta$, and $T_2 = \operatorname E(T_1\mid R)$ is a function of some random variables $X_1, \ldots, X_n$?
I cannot figure out how to use conditioning and the law of total expectation.
We apply conditional Jensen, giving $$ E((T_2-\theta)^2)=E( E(T_1-\theta\mid R)^2)\le E(E((T_1-\theta)^2\mid R)) =E((T_1-\theta)^2)$$ where in the last step we used the law of total expectation.
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