## Density Estimation by Histograms (Part IV)

Today we will apply the ideas of the others post by a simple example. Before, we are going to answer the question of the last week. What is exactly the $latex {h_{opt}}&fg=000000$ if we assume that $latex \displaystyle \displaystyle f(x) = \frac{1}{\sqrt{2\pi}} \text{exp}\left(\frac{-x^2}{2}\right)? &fg=000000$ How $latex {f(x)}&fg=000000$ is the density of standard normal distribution. It is …

## Density Estimation by Histograms (Part III)

Before to continue with today’s post we will answer the question of last week, Is it $latex {\hat{f}_{h}(x)}&fg=000000$ a consistent estimator? The answer is yes. Because convergence in mean squared implies convergence in probability.