STRUCTURAL MULTIVARIATE FUNCTION ESTIMATION - SOME AUTOMATIC DENSITY AND HAZARD ESTIMATES

Structures such as independence of random variables in probability den sities and hazard proportionality in covariate dependent hazard functi ons have important interpretations in statistical analysis. Such struc tures can be characterized by term eliminations from an analysis of va riance (ANOVA) decomposition in log density or log hazard. Nonparametr ic estimation of these functions with an ANOVA decomposition built in can be achieved by using tensor product splines in a penalized Likelih ood approach. In this article, a feasible algorithm with automatic mul tiple smoothing parameters is described to implement this approach, an d examples are presented to illustrate some applications of the techni que. For density estimation, a novel feature is the possibility of ass essing/enforcing independence when data are truncated to a non rectang ular domain. For hazard estimation, models more general than but reduc ible to proportional hazard models are available, and model terms are estimated simultaneously via penalized full likelihood.