## 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, $latex \displaystyle \mathrm{MISE}\triangleq\mathop{\mathbb E}_{p}\int\left(\hat{p} _{n}(x)-p(x)\right)^{2}dx &fg=000000$ …

## Density Estimation by Histograms (Part II)

We continue our presentation about the estimation of histograms and its statistical properties. Today we will start the theory for reducing the mean squared error. In order to study the statistical properties of $latex {\hat{f}_{h}(x)}&fg=000000$We will start introducing the concept of mean squared error (MSE) or quadratic risk. We define