# Month: October 2011

## 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

## Density Estimation by Histograms (Part I)

We are going to introduce the histogram as a simple nonparametric density estimator.  I will divide this presentation in several posts for simplicity reasons. Let us $latex {X_1,\ldots,X_n}&fg=000000$ with pdf $latex {f}&fg=000000$. The histogram is the simplest nonparametric estimator of $latex {f}&fg=000000$.

## Importance of nonparametric statistics in regression.

I would like to start this blog with some basic ideas about density estimation and nonparametric regression. The study of the probability density function (pdf) is called nonparametric estimation. This kind of estimation can serve as a block building in nonparametric regression. The typical regression problem is setting as follows. Assume that we have a …