Mathematical Sciences: Methods for Smoothing Bivariate, Irregularly Spaced Data

数学科学：平滑二变量、不规则间隔数据的方法

• 批准号: 9510435
• 负责人: Karen Kafadar
• 金额: $ 3万
• 依托单位: University of Colorado at Denver-Downtown Campus
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-09-01 至 1996-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9510435&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Methods; Smoothing; Bivariate

9510435 Kafadar Abstract The research under this project will develop methods for smoothing bivariate, irregularly spaced data such as environmental, geological, or health-related data with geographically-defined coordinates. Because such data often arise from non-Gaussian distributions with potentially non-stationary noise (e.g., highly skewed values in barometric pressure data, exotic values due to earthquakes in geophysical data, discontinuities due to faults in geological data), linear smoothers, or smoothers derived assuming stationary white noise, may not perform as well as more robust, nonlinear smoothers in capturing the underlying trend. This research will attempt to identidy (1) those situations where nonlinear versus linear smoothers should yield good performance; (2) how smoothed values at the border should be defined (often a source of significant bias in estimating the trend); and (3) how the resulting smoothed trend can be displayed. In 1974, the National Cancer Institute published the Atlas of Cancer Mortality for U.S. Counties: 1950-1969. It consisted of U.S. maps, one for each of 35 sites of cancer, where counties were shaded according to the level of the mortality rate for the cancer site being depicted. These maps illustrated, for example, high rates of lung cancer around the Gulf of Mexico and high rates of bladder cancer around Delaware and New Jersey; subsequently, environmental causes for these high rates were identified. Further atlases of cancer mortality were published, and an atlas of mortality from causes other than cancer is forthcoming from National Center for Health Statistics. Because some counties have very small populations, reported mortality rates are very uncertain; regions of elevated risks may be difficult to detect. The objective of this research is to develop methods which will highlight geographical patterns in data such as cancer mortality in U.S. counties. Geographical movement of populations often is responsible for spreading the risk around. Thus it is important to identify not just isolated counties of elevated risk but broad regions which may indicate environmental causes for concern. Conversely, regions of low risk may serve as models for measures of disease prevention and control. These methods can be applied to other sorts of data to answer similar questions, such as which regions indicate significant seismic activity, or in which places the ozone layer is depleting most rapidly.

9510435 KAFADAR摘要该项目下的研究将开发用于平滑双变量，不规则间隔的数据的方法，例如环境，地质或与健康相关的数据，并具有地理定义的坐标。 Because such data often arise from non-Gaussian distributions with potentially non-stationary noise (e.g., highly skewed values in barometric pressure data, exotic values due to earthquakes in geophysical data, discontinuities due to faults in geological data), linear smoothers, or smoothers derived assuming stationary white noise, may not perform as well as more robust, nonlinear smoothers in capturing the underlying trend. 这项研究将尝试识别（1）那些非线性与线性smoothorther应该产生良好性能的情况； （2）如何定义边界的平滑值（通常是估计趋势的明显偏见的来源）； （3）如何显示产生的平滑趋势。 1974年，美国国家癌症研究所（National Cancer Institute）出版了美国县的癌症死亡地图集：1950- 1969年。 它由美国地图组成，其中一个是35个癌症部位中的每个地图，该县根据所描绘的癌症部位的死亡率水平来遮蔽县。 这些地图说明了墨西哥湾周围的高肺癌的高率，以及特拉华州和新泽西州周围膀胱癌的高率。随后，确定了这些高率的环境原因。 发表了癌症死亡率的进一步地图，并从国家健康统计中心即将到来的癌症以外的其他原因死亡地图集。 由于某些县人口很少，因此报告的死亡率非常不确定。风险升高的区域可能很难检测到。这项研究的目的是开发方法，该方法将突出数据中的地理模式，例如美国县的癌症死亡率。人口的地理运动通常负责散布风险。 因此，重要的是要确定风险升高的孤立县，而且可能表明令人担忧的环境原因的广泛地区。 相反，低风险区域可以作为预防疾病预防和控制的模型。 这些方法可以应用于其他类型的数据，以回答类似的问题，例如哪些区域表明地震活动显着，或者在哪些地方臭氧层层最快地耗尽。