We seek to develop reliable automatic structural nonparametric estimators of densities and hazards on multidimensional domains. The structure, ANOVA decomposition of functions, can be built in via tensor product splines. For density estimation, the structure allows conditional independence to be built into multivariate densities; for hazard estimation, it yields survival models more general than, but reducible to, proportional hazard models. The targeted results are asymptotic theory and automatic algorithms implemented in portable public domain code. Our research is on the estimation (reconstruction) of curves/surfaces based on imperfect data collected in designed experiments or other scientific studies. The curves/surfaces to be reconstructed may represent geographical distribution of acid rain deposition as is useful for environmental monitoring, or may characterize the effectiveness of medical treatments in clinical trials, etc. Prior results of the research have found applications in modeling weather data, environmental data, and AIDS data.
