Mathematical Sciences: Resampling Methods in Model Selection and Sample Surveys

建议：DMS9504425 PI：邵军学院：大学。威斯康星-麦迪逊的题目：模型选择和样本调查中的重抽样方法摘要：本研究涉及以下几个方面的调查。(1)研究了线性回归、非线性回归、广义线性模型、时间序列和多元分析中各种数据重采样模型选择方法的理论性质。对于现有方法不能令人满意的问题，将开发新的和先进的方法。(2)开发可应用于具有推定缺失值的复杂调查数据的数据重采样方法。这包括修改和调整现有的数据重采样方法，这些方法不适合复杂的调查数据。(3)研究人员对数据重采样方法的理论性质的研究包括对数据重采样方法的渐近(大样本)性质和固定(小)样本性能的研究。将评估不同方法的相对性能。结果将以易于采用的形式给出，作为实际应用的指导。(4)数据重采样方法通常需要对给定的统计量进行重复计算。在模型选择和抽样调查问题中，数据集的规模通常很大，因此一些数据重采样方法所需的计算可能会很繁琐。研究人员研究了一些有效的计算方法。统计分析通常基于一个数据集，该数据集是来自总体的样本，而总体是感兴趣的某些变量的值的集合。由于样本只是总体的一部分，根据样本得出的结论会受到某些统计误差的影响。一种评估统计误差的方法，称为数据重采样法，通过将样本视为总体从样本中提取多个子样本，并将样本与总体之间的类似关系应用于子样本和样本进行推断。这种方法近年来迅速流行起来，因为(1)廉价和快速的计算设施的存在确保了这种计算机密集型方法的实施；(2)这种方法有时提供了比通常使用的传统方法更准确和/或更稳定的解决方案；(3)当所考虑的问题很复杂时，应用传统方法所需的理论推导非常困难。虽然在过去的二十年里，这种方法有了许多发展，但这种技术的新近留下了许多与实际应用相关的问题。这项研究的目的是在各种复杂的统计问题中开发、评估和应用多种类型的数据重采样方法。

Proposal: DMS9504425 PI: Jun Shao Institution: Univ. of Wisconsin - Madison Title: Resampling Methods in Model Selection and Sample Surveys Abstract: This research involves the following areas of investigation. (1) The investigator studies the theoretical properties of various data-resample model selection methods in linear and nonlinear regression, generalized linear models, time series and multivariate analysis. New and advanced methods will be developed in problems where the existing methods lead to unsatisfactory results. (2) Data-resample methods that can be applied to complex survey data with imputed missing values will be developed. This includes modification and adaptation of the existing data-resample methods which are not suitable for complex survey data. (3) The investigator's study of the theoretical properties of the data-resample methods include investigations of the asymptotic (large sample) properties and the fixed (small) sample performances of the data-resample methods. The relative performances of different methods will be assessed. The results will be given in a form which can be easily adopted as a guide for practical applications. (4) The data-resample methods usually require repeated computations of some given statistics. In model selection and sample survey problems the size of the data set is usually large so that the computation required by some data-resample methods may be cumbersome. The investigator studies some efficient methods for computations. Statistical analysis is usually based on a data set that is a sample from a population which is a collection of values of some variable of interest. Since the sample is only a part of the population, conclusions drawn based on the sample are subject to certain statistical errors. A method for assessing statistical errors, called the data-resample method, takes many sub-samples from the sample by treating the sample as the population, and makes inference by applying th e analogous relationships between the sample and the population to the sub-samples and the sample. This method has caught on very rapidly in recent years because (1) the existence of inexpensive and fast computing facilities ensures that this computer-intensive method can be implemented; (2) this method sometimes provides more accurate and/or stable solutions than the traditional methods that are commonly used; (3) the theoretical derivations required in applying the traditional methods are very difficult when the problem under consideration is complex. Although there are many developments in using this method over the last two decades, the recency of this technique has left many questions unanswered which are relevant to practical application. The aims of this research are in the area of development, evaluation, and application of many types of data-resample methods in various complex statistical problems.