Mathematical Sciences: A Study of Nonparametric Curve Estimators

该研究的总体主旨是提供一种非参数替代响应面方法中使用的当前参数方法。非参数方法基于核估计量。一个测试将开发的有效性的一般加性模型对非参数替代。在半参数模型的情况下，该模型对响应变量和几个协变量之间关系的确定性部分进行建模，一些协变量将包括在参数部分，其余协变量将包括在非参数部分。然后，将对假设的半参数模型对非参数替代方案的有效性进行检验。在为回归函数的核估计选择带宽时，假设给出了未知回归函数的导频估计，将开发一种分析和方法，用于选择在交叉验证类型过程中遗漏的最佳点数。

The overall thrust of the research is to provide a nonparmetric alternative to current parametric approaches used in response surface methodology. The nonparametric methodology is based on kernel estimators. A test will be developed for the validity of the general additive model against a nonparametric alternative. In the case of a semiparametric model which models which models the deterministic part of the relationship between a response variable and several covariates, some covariates will be included in a parametric portion and the remaining covariates in a nonparametric portion. Then a test will be developed for the validity of the postulated semiparametric model against a nonparametric alternative. In choosing bandwidths for kernel estimates of a regression function, an analysis and method for choosing the optimal number of points to leave out of a cross validation type procedure will be developed assuming a pilot estimate of the unknown regression function is given.