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.
