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; some error analysis. An example with data from the homework. Estimating conditional densities; another example with homework data. Some issues with likelihood, maximum likelihood, and non-parametric estimation.
Posted at February 04, 2011 01:35 | permanent link