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Convergence of series, sequences and functions and different modes of convergence.

2 votes
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Convergence of estimator given by a fixed point

Let $X$ be a non-negative random variable with cdf $F$ and define $$G(s) = E[\max(0,u(X)-sX)],$$ where $u$ is some real function. Let $s_0$ be the unique fixed point of $G$. Now let $X_1,\dots,X_t$ b …
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