Mathematical Sciences: Problems in Statistical Modeling

数学科学：统计建模问题

• 批准号: 9002791
• 负责人: David Ruppert
• 金额: --
• 依托单位: Cornell University
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-01 至 1993-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9002791&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Problems; Statistical; Modeling

Stochastic approximation techniques will be applied to develop computational algorithms for the statistical analysis of spatial processes and for the control of laboratory instruments. Both the practical implementation and theoretical properties of the algorithms will be investigated. New methods for locating variable-stabilizing transformations will be studied. These methods will be based on a nonparametric estimate of the variance function. These new techniques are promising for multivariate transformation families such as the shifted-power transformations and nonparametric spline transformations. Transformations will also be investigated in the context of density estimation. The method to be investigated consists of transforming the data to a density that can be accurately estimated by a kernel estimator, applying a kernel estimator, and transforming this estimate back to the original space to estimate the density of the original data. Source appointment is a methodology for attributing pollution to its sources by chemical mass balance. Source apportionment when the composition of one source is unknown will be investigated. Nonlinear regression will be studied when there are measurement errors in the independent variables and no replication.

随机近似技术将应用于 开发用于统计分析的计算算法， 空间过程和实验室仪器的控制。 的实际实现和理论特性， 将研究算法。 新的定位方法 将研究变量稳定化变换。 这些 方法将基于方差的非参数估计 功能 这些新技术对于多变量 变换族，例如移位幂变换 和非参数样条变换。 转变将 也可以在密度估计的背景下进行研究。 的 方法是将数据转换为 可以通过核估计器精确估计的密度， 应用核估计器，并将该估计转换回 到原始空间来估计原始的密度 数据源指定是一种方法， 通过化学物质平衡对污染源进行控制。 源 当一个来源的组成不明时， 追究 非线性回归将在以下情况下进行研究 是独立变量的测量误差， 复制的