  It is possible to approach regression analysis with random covariates from a
semiparametric perspective where information is combined from multiple
multivariate sources. The approach assumes a semiparametric density ratio model
where multivariate distributions are "regressed" on a reference distribution. A
kernel density estimator can be constructed from many data sources in
conjunction with the semiparametric model. The estimator is shown to be more
efficient than the traditional single-sample kernel density estimator, and its
optimal bandwidth is discussed in some detail. Each multivariate distribution
and the corresponding conditional expectation (regression) of interest are
estimated from the combined data using all sources. Graphical and quantitative
diagnostic tools are suggested to assess model validity. The method is applied
in quantifying the effect of height and age on weight of germ cell testicular
cancer patients. Comparisons are made with multiple regression, generalized
additive models (GAM) and nonparametric kernel regression.
