Optimal Bayesian Estimation of a Regression Curve, a Conditional Density, and a Conditional Distribution

Conditional Density Estimation in a Regression Setting

Regression problems are traditionally analyzed via univariate characteristics like the regression function, scale function and marginal density of regression errors. These characteristics are useful and informative whenever the association between the predictor and the response is relatively simple. More detailed information about the association can be provided by the conditional density of th...

Conditional density estimation in a censored single-index regression model

Nonparametric Conditional Density Estimation in a High-Dimensional Regression Setting

In some applications (e.g., in cosmology and economics), the regression E[Z|x] is not adequate to represent the association between a predictor x and a response Z because of multi-modality and asymmetry of f(z|x); using the full density instead of a singlepoint estimate can then lead to less bias in subsequent analysis. As of now, there are no effective ways of estimating f(z|x) when x represen...

A geometric framework for density estimation and conditional density estimation

We introduce a geometrically intuitive procedure to obtain an estimator for a probability density function in the absence or presence of predictors. The estimation procedure is based on starting with an initial estimate of the density shape and then transforming it via a warping function to obtain the final estimate. The idea is to design the initial estimate to be computationally fast, albeit ...

Smoothing Spline Density Estimation : Conditional Distribution

This article extends recent developments in penalized likelihood probability density estimation to the estimation of conditional densities on generic domains. Positivity and unity constraints for a probability density are enforced through a one-to-one logistic conditional density transform made possible by term trimming in an ANOVA decomposition of multivariate functions. The construction of mo...