Adaptive Regression for Dependent Data by Combining Different Procedures

本建议涉及随机误差相关时自适应回归的研究和教育。基于不同的假设，已经（并将）提出了许多非参数回归的方法。在实际应用中，用户经常面临的一个难题是如何选择最佳的数据处理方法。尤其是对于高维函数估计，为了克服维度灾难，根据目标函数的不同特征，提出了投影寻踪、CART、神经网络、加性模型、MARS等各种简约模型。在这项研究中的一个主要兴趣是通过结合候选程序的集合来构造自适应估计。组合过程的目标是自动执行和（或接近）最好的原始过程一样好，而不知道它是哪一个。 随机误差将被假定为通常是相关的，包括短期和长期的情况。研究了依赖性对适应能力的影响。可以预见的是，理论上证明和计算上可行的算法将被提出来结合联合收割机回归过程，针对回归函数的各种特性和随机误差的不同依赖结构，函数估计是一种重要的统计工具，试图根据数据准确地理解变量之间的函数关系，它在许多学科中成功地解决了科学问题。在现实中，观测总是受到来自不同来源的随机噪声（误差）的影响。当随机误差相互依赖时，这种依赖性可能掩盖了兴趣函数关系。长距离相关性是指即使错误发生在彼此远离的时间或地点，错误仍然高度相关的情况。众所周知，这种长程相关性使得目标函数的估计更加困难。在实际应用中，误差之间的相关程度通常是未知的，这使得函数估计问题更加困难。在这个建议中，我们打算开发的方法，自适应地消除不同程度的依赖之间的错误，使thefunctionofinterest可以估计最佳，而不知道的依赖结构的错误。研究结果和相关的工作，由他人对长期依赖的数据将带来给学生在不同层次的几个prosticeses。将与爱荷华州立大学的几位教授及其大气科学、电气工程、农学和可能的其他领域的学生进行合作，以适当地解决长期依赖现象，这种现象经常遇到，并且已知会在现有统计方法的数据分析中造成问题。

This proposal concerns research and education on adaptive regressionwhen the random errors are dependent. Many procedures have been (and will be) proposed for nonparametric regression based ondifferent assumptions. In applications, a difficulty a user oftenfaces is the choice of the best method for the data athand. This is specially the case for high-dimensional functionestimation, where to overcome the curse of dimensionality, various parsimonious models such as projection pursuit, CART, neural nets, additive models, MARS, etc. are proposed according to different characterizations of the target function. A main interest in this research is to construct adaptive estimators by combining acollection of candidate procedures. The goal for the combinedprocedure is to perform automatically as well as (or nearly as wellas) the best original procedure without knowing which one it is. The random errors will be assumed to be generally dependent,including both short- and long-range cases. The effects ofdependence on adaptation capability will be studied. It isanticipated that theoretically proven and computationally feasible algorithms will be proposed to combine regression procedurestargeted at various characteristics of the regression function and different dependence structures for the random errors.Function estimation is an important statistical tool that tries tounderstand accurately the functional relationships between variables based on data and it has applications in many disciplines for successfully addressing scientific questions. In reality, observations are alwayssubject to random noise (error) from different sources. When therandom errors are dependent on each other, the dependence maydisguise the functional relationship of interest. Long-rangedependence refers to a situation where the errors are still highlycorrelated even when they occur at times or locations that are faraway from each other. It is known that such a long-range dependence makesthe estimation of the target function much harder. In applications,the degree of dependence between the errors is usually unknown,which makes the function estimation problem even harder. In thisproposal, we intend to develop methods that adaptively handledifferent degrees of dependence among the errors so that thefunction of interest can be estimated optimally without knowing thedependence structure of the errors. The research results and relatedwork by others on long-range dependent data will be brought tostudents at various levels in several statisticscourses. Collaborations will be conducted with several professors atIowa State University and their students in atmospheric science, electrical engineering, agronomy and possibly other fields toappropriately address long-range dependence phenomena, which havebeen encountered often and known to cause problems in data analysis with the existing statistical methods.