Mathematical Sciences: Problems in Statistical Modeling

随机近似技术将应用于开发空间过程的统计分析和实验室仪器控制的计算算法。本文将研究这些算法的实际实现和理论性质。将研究定位变量稳定变换的新方法。这些方法将基于方差函数的非参数估计。这些新技术在多变量变换族如移幂变换和非参数样条变换中具有广阔的应用前景。变换也将在密度估计的背景下进行研究。所研究的方法包括将数据转换为可以由核估计器精确估计的密度，应用核估计器，并将该估计转换回原始空间以估计原始数据的密度。污染源指定是一种通过化学质量平衡将污染归因于污染源的方法。当一个源的组成未知时，将研究源的分配。当自变量存在测量误差且无复制时，将研究非线性回归。

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.