## Paper’s review: Zhu & Fang, 1996. Asymptotics for kernel estimate of sliced inverse regression.

It is already known, that for $latex { Y\in {\mathbb R} }&fg=000000$ and $latex { X \in {\mathbb R}^{p} }&fg=000000$, the regression problem $latex \displaystyle Y = f(\mathbf{X}) + \varepsilon, &fg=000000$ when $latex { p }&fg=000000$ is larger than the data available, it is well-known that the curse of dimensionality problem arises. Richard E. Bellman …

## The Delta Method: Applications

This week I am going to present three applications of the Delta method theorem. The first is a direct one and it is about the behavior in distribution of the sample variance. The second one is an hypothesis test in the variance when the sample is normal. Finally, the third is an interesting application in …

## Weak Law of Large Numbers and Central Limit Theorem via the Levy’s continuity theorem

The Levy’s continuity theorem is a very important tool in the statistical machinery. For example, it will give us two simple proofs to two classical statistical problems: The Law of Large Numbers and the Central Limit Theorem.

## 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 …