A global measure of risk for kernel estimators in Nikolski classes

Photos of Sergey Nikolskii from The Russian Academy of Sciences The MSE  gives an error of the estimator $latex {\hat{p}_{n}}&fg=000000$ at an arbitrary point $latex {x_{0}}&fg=000000$, but it is worth to study a global risk for $latex {\hat{p} _{n}}&fg=000000$. The mean integrated squared error (MISE) is an important global measure, $latex \displaystyle \mathrm{MISE}\triangleq\mathop{\mathbb E}_{p}\int\left(\hat{p} _{n}(x)-p(x)\right)^{2}dx &fg=000000$ […]