Mathematical Sciences: Bandwidth Selection in Semiparametric Regression Problems

数学科学：半参数回归问题中的带宽选择

• 批准号: 9423247
• 负责人: Naisyin Wang
• 金额: $ 1.8万
• 依托单位: Texas A&M Research Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-06-15 至 1997-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9423247&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Bandwidth; Selection; Semiparametric

9423247 Wang Abstract This project investigates bootstrap bandwidth selection procedures in semiparametric regression models. As pointed out in Hsieh and Manski (1987), the performance of the estimated regression parameter in a semiparametric regression model could be rather sensitive to the choice of bandwidth. The traditional plug-in method often requires estimating elements within a complicated second order expansion of the estimated regression parameter. The fact that the properly chosen bootstrap procedure could estimate these complicated terms in an automatic fashion makes this procedure especially appealing. Two classes of semiparametric regression models are considered here: (i) semiparametric heteroscedastic regression models, and (ii) semiparametric measurement error regression models. Different resampling strategies from those in the parametric and nonparametric regressions have to be pursued due to the different semiparametric structure. Resampling strategies for the aforementioned two semiparametric settings are proposed. Properties of the proposed bandwidth estimators are investigated theoretically as well as numerically. The availability of high-speed computing has allowed researchers to use "semiparametric modeling," a new mathematical development which, for most scientific explorations, is preferable to its traditional parametric rivals because of much greater flexibility. Some recent applications of semiparametric modeling include studies which compare the effects of high versus low AZT treatments on the survival of AIDS patients, the investigation of effects of saturated fat on breast cancer based on self-support food questionnaires and on detailed food records, the relationship between a patient's age at the time of bone-marrow transplant and the incidence of chronic graft versus host disease (GVHD) afterwards. One of the major difficulties in semiparametric modeling is to properly choose a so-called "bandwidth" which controls the amount of data going into the model simultaneously.. Poor choice can result in loss of information or loss of accuracy. This project investigates bandwidth selection procedures which would be theoretically sound and practically feasible. The main approach emphasizes taking advantage of modern computing power to help users to avoid complicated mathematical derivations. Success of this project will certainly further promote the applications of semiparametric modeling in many other fields.

9423247王摘要 本计画探讨半参数回归模型中自举频宽的选取方法。正如Hsieh和Manski（1987）所指出的，半参数回归模型中估计的回归参数的性能对带宽的选择相当敏感。传统的插入法往往需要在估计的回归参数的复杂的二阶展开中估计元素。正确选择的引导程序可以自动估计这些复杂的条款，这使得这个过程特别有吸引力。本文研究了两类半参数回归模型：（i）半参数异方差回归模型和（ii）半参数测量误差回归模型。 由于半参数结构的不同，在参数和非参数回归中必须采取不同的回归策略。提出了上述两个半参数设置的恢复策略。 所提出的带宽估计的性质进行了研究，理论和数值。 高速计算的可用性使研究人员能够使用“半参数建模”，这是一种新的数学发展，对于大多数科学探索来说，由于更大的灵活性，它比传统的参数模型更可取。半参数模型的一些最新应用包括比较高与低AZT治疗对艾滋病患者生存的影响的研究，基于自助食物问卷和详细的食物记录调查饱和脂肪对乳腺癌的影响，骨髓移植时患者年龄与慢性移植物抗宿主病（GVHD）发生率之间的关系。半参数建模的主要困难之一是正确选择所谓的“带宽”，它控制同时进入模型的数据量。糟糕的选择可能会导致信息丢失或准确性损失。本计画探讨频宽选择的程序，理论上是合理的，实际上是可行的。 主要的方法强调利用现代计算能力来帮助用户避免复杂的数学推导。该项目的成功必将进一步推动半参数建模在其他领域的应用。