Mathematical Sciences: Optimal Design of Experiments and Spline Smoothing

数学科学：实验优化设计和样条平滑

• 批准号: 9301511
• 负责人: William Studden
• 金额: $ 6.9万
• 依托单位: Purdue Research Foundation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-07-01 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9301511&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Optimal; Design; Experiments

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.

我们寻求开发可靠的自动结构非参数估计的密度和危险的多维域。 函数的ANOVA分解结构可以通过张量积样条来构建。 对于密度估计，该结构允许将条件独立性构建到多变量密度中;对于风险估计，它产生比比例风险模型更一般的生存模型，但可还原为比例风险模型。 目标的结果是渐近理论和自动算法实现在便携式公共领域的代码。 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的曲线/曲面的估计（重建）。 要重建的曲线/表面可以代表酸雨沉积的地理分布，是有用的环境监测，或可以表征的有效性，在临床试验中的医学治疗等先前的研究结果已经发现应用建模天气数据，环境数据和艾滋病数据。