Mathematical Sciences: Resampling Methods in Model Selection and Sample Surveys

提案：DMS 9504425 PI：Jun Shao机构：威斯康星州-麦迪逊大学标题：模型选择和样本调查中的恢复方法 摘要： 本研究涉及以下调查领域。 (1)研究人员研究了各种理论性质， 线性和非线性回归中的数据重采样模型选择方法， 广义线性模型、时间序列和多变量分析。 新的和先进的方法将被开发的问题，现有的方法导致不满意的结果。(2)数据重采样方法，可应用于具有插补的复杂调查数据 将开发缺失值。这包括修改和 修改现有的不适用的数据重采样方法 复杂的调查数据。(3)研究者对数据重采样方法的理论性质的研究包括调查 渐近（大样本）性质和固定（小） 数据重采样方法的样本性能。的相对 将评估不同方法的性能。结果 将以一种易于采用的形式给出， 实际应用等(4)数据重采样方法通常需要 重复计算一些给定的统计数据。在模型选择和 抽样调查问题数据集的大小通常很大， 某些数据重采样方法所需的计算可能很麻烦。 研究者研究了一些有效的计算方法。 统计分析通常基于数据集，该数据集是来自总体的样本，该总体是一些感兴趣的变量的值的集合。由于样本只是人口的一部分，结论 根据样本得出的数据存在一定的统计误差。 一种估计统计误差的方法称为数据重抽样法，它把样本看作总体，从样本中抽取许多子样本，利用类比关系进行推理 从样本和总体到子样本和样本。这种方法近年来迅速流行起来， (1)廉价和快速的计算设施的存在确保了 这种计算机密集型的方法可以实现;（2）这 方法有时提供更准确和/或更稳定的解决方案比 传统的常用方法;（3）理论推导 当所考虑的问题复杂时，应用传统方法所需的参数是非常困难的。虽然有很多发展 在使用这种方法在过去的二十年里， 技术留下了许多与实际应用有关的问题没有得到解答。 应用程序.这项研究的目的是在发展领域， 评价和应用多种类型的数据重采样方法， 各种复杂的统计问题。

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.