Optimal Convergence Properties of Variable Knot, Kernel, and Orthogonal Series Methods for Density Estimation
Optimal Convergence Properties of Variable Knot, Kernel, and Orthogonal Series Methods for Density Estimation
Let $W_p^{(m)}(M) = \{f: f^{(\nu)} \operatorname{abs}. \operatorname{cont}., \nu = 0, 1,\cdots, m - 1, f^{(m)} \in \mathscr{L}_p, \|f^{(m)}\|_p \leqq M\}$, where $\|\cdot\|_p$ is the norm in $\mathscr{L}_p, m$ is a positive integer and $p$ is a real number, $p \geqq 1$. Let $\{\hat{f}_n(x)\}, n = 1, 2,\cdots$ be any sequence …