On Minimax Estimation in the Presence of Side Information About Remote Data
远端数据辅助信息下的极小极大估计
We analyze the following model: One person, called "helper" observes an outcome $x^n = (x_1, \cdots, x_n) \in \mathscr{X}^n$ of the sequence $X^n = (X_1, \cdots, X_n)$ of i.i.d. RV's and the statistician gets a sample $y^n = (y_1, \cdots, y_n)$ of the sequence $Y^n(\theta, x^n)$ of RV's with a density $\prod^n_{t = 1} f(y_t \mid \theta, x_t)$. The helper can give some (side) information about $x^n$ to the statistician via an encoding function $s_n: \mathscr{X}^n \rightarrow \mathbb{N}$…