Constrained Nonparametric Inference and Data Visualization through Data Sharpening

拟议的研究旨在改进平滑数据的方法，以便更清楚地显示其中所含的信息。 为了从数据中提取有用的信息，有必要以图形方式对其进行探索，特别是在有许多观察结果的情况下。 核平滑方法提供了数据的图形摘要，允许数据分析人员检测模式和变量之间可能的关系，并且分析是以这样一种方式进行的，即需要做出很少的假设，允许数据“为自己说话”。 在许多情况下，关于数据的附加信息是可用的。 例如，森林火灾燃烧的面积不会随着火灾燃烧的时间而减少。 因此，在对野火的增长进行建模时，除了观察到的测量之外，我们还可以使用这些信息。 标准技术，如果没有调整，通常会忽略这些信息，产生的模型有时会产生与现实不符的异常。 拟议研究的一个特别重点将是数据锐化，这是一种数据调整技术，利用有关数据或产生数据的过程的额外信息。 然后将标准统计技术应用于调整后的数据，以便在不影响统计性能的情况下纳入给定的信息。计划是优化平滑方法，并对使用数据锐化的统计推断方法展开全面调查。 后者的技术将导致改进的不确定性量化的应用，如野火预测。 数据锐化福尔斯分为两类：“监督”和“无监督”。在前者中，数据被移动最小的距离，受到额外的信息被满足的结果模型。 例如，我们可能希望最小限度地移动火灾大小测量值，前提是最终模型只能预测火灾大小随时间增加。 无监督数据锐化不直接包含外部信息，而是与给定统计技术的属性一起工作，以提出调整数据的规则，从而提高结果估计的准确性。 早就应该对数据锐化及其变体进行彻底调查，因为该方法是在一段时间前提出的，但根本没有得到充分探讨，而且它在改善各种统计方法的性能方面有很大的希望。 该提案中开发的方法也将立即用于重要的应用，包括：对空中加油机飞行员疲劳因素的研究，其中研究了反应时间数据，生理变量和环境变量;金融信贷风险问题;以及如上所述，由于野火等现象造成的环境风险。

The proposed research seeks to improve upon methods for smoothing data in order to more clearly visualize the information contained therein. In order to extract useful information from data, it is necessary to explore it graphically, especially in situations where there are many observations. Kernel smoothing methods provide graphical summaries of data which allow a data analyst to detect patterns and possible relationships between variables, and the analysis is done in such a way that very few assumptions need to be made, allowing the data to "speak for themselves''. In many circumstances, additional information about the data is available. For example, the area burned by a forest fire will not decrease over the time that the fire is burning. Therefore, when modelling the growth of a wildfire, we could use this information in addition to observed measurements. Standard techniques, without adjustment, usually ignore this information, and the resulting models can sometimes produce anomalies that do not match reality. A particular focus of the proposed research will be on data sharpening which is a data-adjustment technique where extra information about the data, or the process that gave rise to the data, is exploited. Standard statistical techniques are then applied to the adjusted data, so that the given information is incorporated, without compromising statistical performance. The plan is to optimize the methodology for smoothing and to launch a full-scale investigation into statistical inference methods that use data sharpening. The latter techniques will lead to improved uncertainty quantification in applications such as wildfire prediction. Data sharpening falls into two categories: "supervised" and "unsupervised". In the former, data are moved a minimal distance, subject to the extra information being satisfied by the resulting model. For example, we might want to move fire size measurements minimally, subject to the requirement that the resulting model only predicts that fire size increases over time. Unsupervised data sharpening does not directly incorporate external information but rather works with properties of the given statistical technique to come up with rules for adjusting the data so that accuracy of the resulting estimate is improved. A thorough investigation of data sharpening and its variants is overdue, since the methodology was proposed some time ago but not at all fully explored, and since it holds considerable promise in terms of improving performance of a wide variety of statistical methods. The methodologies developed in the proposal will also immediately be put to use in important applications including: a study of factors underlying airtanker pilot fatigue, where reaction time data, physiological variables, and environmental variables are studied; problems in financial credit risk; and, as alluded to above, environmental risk due to phenomena such as wildfire.