Multiscale likelihood analysis and complexity penalized estimation

Multiscale Likelihood Analysis and Complexity Penalized Estimation

We describe here a framework for a certain class of multiscale likelihood factorizations wherein, in analogy to a wavelet decomposition of an L function, a given likelihood function has an alternative representation as a product of conditional densities reflecting information in both the data and the parameter vector localized in position and scale. The framework is developed as a set of suffic...

Lectures 12 and 13 - Complexity Penalized Maximum Likelihood Estimation

As you learned in previous courses, if we have a statistical model we can often estimate unknown “parameters” by the maximum likelihood principle. Suppose we have independent, but not necessarily identically distributed, data. Namely, we model the data {Yi}i=1 as independent random variables with densities (with respect to a common dominating measure) given by pi(·; θ), where θ is an unknown “p...

Penalized Likelihood Density Estimation :

Penalized Likelihood Estimation: Convergence under Incorrect Model

Penalized likelihood method is among the most eeective tools for nonparametric multivari-ate function estimation. Recently, a generic computation-oriented asymptotic theory has been developed in the density estimation setting, and been extended to other settings such as conditional density estimation, regression, and hazard rate estimation, under the assumption that the true function resides in...

Penalized Likelihood Estimation in Gaussian Mixture Models