### Density Estimation (Advanced Data Analysis from an Elementary Point of View)

The desirability of estimating not just conditional means, variances, etc.,
but whole distribution functions. Parametric maximum likelihood is a solution,
if the parametric model is right. Histograms and empirical cumulative
distribution functions are non-parametric ways of estimating the distribution:
do they work? The Glivenko-Cantelli law on the convergence of empirical
distribution functions, a.k.a. "the fundamental theorem of statistics". More
on histograms: they converge on the right density, if bins keep shrinking but
the number of samples per bin keeps growing. Kernel density estimation and its
properties: convergence on the true density if the bandwidth shrinks at the
right rate; superior performance to histograms; the curse of dimensionality
again. An example with cross-country economic data. Kernels for discrete
variables. Estimating conditional densities; another example with the OECD
data. Some issues with likelihood, maximum likelihood, and non-parametric
estimation.

*Reading*: Notes, chapter 15

Advanced Data Analysis from an Elementary Point of View

Posted by crshalizi at March 08, 2012 10:30 | permanent link