Nonparametric Estimation in Engineering

DMS 9626762 Ruppert研究条件期望、条件方差和条件密度的非参数估计，即不假设这些函数属于参数家族的估计。这项工作使用了局部回归，这是一种特别简单和有效的非参数方法，其中一个人在函数域中的每个点上对参数模型进行局部拟合，以便估计该点上的函数。通过改变点，可以得到一个全局非参数估计量。“局部性”的程度是通过带宽或平滑参数实现的。这项工作包括(A)多元局部多项式回归，其中局部邻域由必须估计的对称的正定带宽矩阵来确定；(B)用于估计具有极点、跳跃不连续或不连续导数的函数的非多项式局部模型；以及(C)通过估计方程的局部拟合来估计相关函数和其他具有科学意义的函数的半参数估计。目前非参数估计研究的应用主要集中在工程领域，但也包括营养学方面的研究。这些应用包括计算机图形学中的密度估计辐射度，对湍流建模的pdf方法的模拟数据的分析，金融工程中的挥发性估计，结合局部回归平滑和克里格法进行空间数据分析，以及对食物频率问卷测量的营养吸收与更准确但也更昂贵的食物记录之间的相关性进行建模。在环境科学的战略领域，这项工作已被应用于两种截然不同的空气污染监测方法--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. ***