Nonparametric Regression

摘要：重点研究了(a)基于惩罚方法的回归样条拟合，(b)基于回归样条的贝叶斯非参数推理，(c)多元回归样条在随机动态规划中的应用，以及(d)局部回归中的带宽选择。回归是一种统计技术，用于发现变量之间的关系，例如，饮食中饱和脂肪的百分比和癌症的可能性。回归在科学和工程中得到了广泛的应用。现代回归方法，包括本研究，关注的是具有大量变量的复杂非线性关系。一个典型的例子是基于信用申请人的整个信用历史和其他财务变量来估计信用风险。本研究将是非参数回归，这意味着必须从数据中发现关系的形式。非参数回归技术以“数据挖掘”的名义在商业中迅速得到应用。在SRC资助的另一个项目中，该研究将应用于半导体制造中工具利用率的提高。

Proposal Number: DMS 9804058 PI: David Ruppert Institution: Cornell University Project: Nonparametric Regression Abstract: The research focuses on (a) fitting regression splines by penalized methods, (b) Bayesian nonparametric inference using regression splines, (c) multivariate regression splines with applications to stochastic dynamic programming, and (d) bandwidth selection in local regression. Regression is a statistical technique for discovering relationships between variables, for example, percentage of saturated fat in one's diet and the probability of cancer. Regression is applied thoroughout the sciences and engineering. Modern regression methodology, including this research, focuses on complex nonlinear relationships with large numbers of variables. A typical example would be estimation of credit risk based upon an entire credit history and other financial variables of a credit applicant. This research will be on nonparametric regression meaning that the form of the relationship must be discovered from the data. Nonparametric regression techniques are rapidly finding applications in business under the name "data mining." In a separate project funded by the SRC, the research will be applied to the improvement of tool utilization in semiconductor manufacturing.