Mathematical Sciences: Optimal Design of Experiments and Spline Smoothing

我们寻求开发可靠的多维域密度和危险的自动结构非参数估计器。结构，方差分析分解函数，可以建立在通过张量积样条。对于密度估计，该结构允许将条件独立性构建到多元密度中；对于风险估计，它产生的生存模型比比例风险模型更一般，但可简化为比例风险模型。目标结果是在可移植的公共领域代码中实现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善数据对曲线/曲面的估计（重建）。要重建的曲线/曲面可以代表酸雨沉积的地理分布，这对环境监测很有用，或者可以表征临床试验中医学治疗的有效性等。先前的研究结果已经在天气数据、环境数据和艾滋病数据的建模中得到了应用。

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.