. Available from the website for this book are some manifold data exhibiting some strong structure. Specifically, these four-dimensional data come from a mixture distribution, with a low weighting of...

.
Available from the website for this book are some manifold data exhibiting some strong structure. Specifically, these four-dimensional data come from a mixture distribution, with a low weighting of a density that lies nearly on a three-dimensional manifold and a high weighting of a heavy-tailed density that fills four-dimensional space.

a.
Estimate the direction of the least normal univariate projection of these data. Use a sequence of graphs to guess a nonnormal projection direction, or followthe method described for the projection step of exploratory projection pursuit.

b.
Estimate the univariate density of the data projected in the direction found in part (a), using any means you wish.

c.
Use the ideas in this chapter to estimate and/or describe the density of these data via any productive means. Discuss the difficulties you encounter