Mathematical Sciences: Optimal Design of Experiments and Spline Smoothing

我们寻求开发多维域上密度和危险的可靠的自动结构非参数估计。这种结构，即函数的ANOVA分解，可以通过张量积样条来构建。对于密度估计，该结构允许在多变量密度中建立条件独立性；对于风险估计，它产生比比例风险模型更一般但可简化的生存模型。目标结果是在可移植的公共领域代码中实现的渐近理论和自动算法。我们的研究是基于设计实验或其他科学研究中收集的不完美数据来估计(重建)曲线/曲面。要重建的曲线/曲面可以表示酸雨沉积的地理分布，这对于环境监测是有用的，或者可以表征临床试验中的医疗效果等。先前的研究结果已被应用于对天气数据、环境数据和艾滋病数据进行建模。

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.