A Lower Bound on the Error in Nonparametric Regression Type Problems
A Lower Bound on the Error in Nonparametric Regression Type Problems
Let $(X_1, Y_1), \cdots, (X_n, Y_n)$ be a sample, denote the conditional density of $Y_i\mid X_i = x_i$ as $f(y\mid x_i, \theta(x_i))$ and $\theta$ an element of a metric space $(\Theta, d)$. A lower bound is provided for the $d$-error in estimating $\theta$. The order of the bound depends on …