Nonparametric Estimation in Engineering

DMS 9626762 Ruppert 研究了条件期望、条件方差和条件密度的非参数估计， 估计，而不假设这些函数属于参数族。 这项工作使用局部回归，一个特别简单和有效的非参数方法，其中一个适合参数模型局部在域中的每个点的功能，以估计在该点的功能。 通过改变点，可以实现全局非参数估计。 “局部性”的程度通过带宽或平滑参数来实现。 工作包括（a）多元局部多项式回归，其中局部邻域由必须估计的对称正定带宽矩阵确定;（B）非多项式局部模型，用于估计具有极点、跳跃不连续或不连续导数的函数;以及（c）通过估计方程的局部拟合对相关函数和其他科学感兴趣的函数进行半参数估计。 本研究的非参数估计目前的应用主要是在工程，但包括营养。 这些应用包括计算机图形学中的密度估计辐射度，从湍流建模的pdf方法中分析模拟数据，估计金融工程中的挥发性，结合局部回归平滑和克里格空间数据分析，以及通过食物频率问卷和更准确但也更昂贵的食物记录测量的营养摄取之间的相关性建模。 在环境科学的战略领域，这项工作已被应用于两种非常不同的监测空气污染的方法，激光雷达和生物监测。 ***

DMS 9626762 Ruppert The research is on nonparametric estimation of conditional expectations, conditional variances, and conditional densities, i.e., estimation without assuming that these functions belong to a parametric family. The work uses local regression, a particularly simple and effective nonparametric method, where one fits parametric models locally at each point in the domain of the function in order to estimate the function at that point. By varying the point one achieves a globally nonparametric estimator. The degree of "localness" is achieved by a bandwidth or smoothing parameter. The work includes (a) multivariate local polynomial regression where the local neighborhoods are determined by a symmetric, positive definite bandwidth matrix that must be estimated; (b) non-polynomial local models for estimating functions with poles, jump discontinuities, or discontinuous derivatives; and (c) semiparametric estimation of correlation functions and other functions of scientific interest by local fitting of estimating equations. %%% Present applications of this research on nonparametric estimation are mostly in engineering but include nutrition. These applications include density-estimation radiosity in computer graphics, analysis of simulation data from the pdf method of modeling turbulence, estimating volatilities in financial engineering, combining local regression smoothing and kriging for spatial data analysis, and modeling the correlation between nutrient uptake as measured by both food frequency questionnaires and more accurate, but also more expensive, food records. In the strategic area of environmental science, this work has been applied to two very different methods of monitoring air pollution, LIDAR and biomonitoring. ***