Approximate and Exact Inference Via Computer-Intensive Methods

研究者将继续开发不依赖于不现实或无法验证的模型假设的推理方法。标准推理方法依赖于强假设，特别是在时间序列，随机场的分析中，或者必须考虑复杂依赖关系的时候。相比之下，再抽样、二次抽样和其他计算机密集型方法提供了可行的方法来获得有效的分布近似，同时对生成数据的随机机制假设很少。在本提案的第1部分中，研究者将解决几个重要问题，以便这些自举和二次抽样方法可以在统计实践中作为良好的近似方法。我们希望处理的主要问题包括：（如长记忆数据的混合速率较慢，并考虑到非平稳性）;不规则间隔数据的更多理论;研究收敛速率取决于未知参数的微妙问题，如具有单位根的自回归型过程的众所周知的困难问题;通过Richardson外推等技术和通过最佳选择区组大小来提高分布估计的准确性;并在相关数据情况下开发拟合优度检验。由于非线性和非平稳性所带来的固有困难，这些方法在经济时间序列建模中特别有用。在提案的第2部分，研究者将致力于开发具有精确有限样本有效性的方法，例如保守置信区域的构建，而不会损失效率，至少在大样本中是这样。典型的非参数方法基于近似或极限定理，因此有限样本行为始终是一个问题，并且通常通过小规模模拟来解决。数据的统计分析在许多不同的科学学科中是至关重要的：物理学、工程学、声学、地质统计学、医学、计量经济学、地震学、法学、生态学等。现代统计分析的范围在不断扩大，同时也需要在不强加强有力的模型假设的情况下有效的推理方法。 研究人员将继续追求发展的统计方法，可以安全地应用于实践中，牢记许多应用程序，这些方法可以卓有成效地应用。 研究者的哲学方法是开发具有稳健有效性的实用方法，以便它们可以应用于日益复杂的情况。这项工作的影响可能是相当大的，因为强有力的推理陈述可以不强加强有力的假设。

The investigator will continue the development of inferential methods that do not rely on unrealistic or unverifiable model assumptions. Standard inferential methods rest upon strong assumptions, especially in the analysis of time series, random fields, or whenever complex dependencies must be taken into account. In contrast, resampling, subsampling, and other computer-intensive methods offer viable approaches to obtaining valid distributional approximations while assuming very little about the stochastic mechanism generating the data. In part 1 of this proposal, the investigator will address several important problems so that these bootstrap and subsampling methods can serve as good approximate methods in statistical practice. The main issues we wish to tackle include the following: further relaxing of conditions (such as slower mixing rate for long memory data and allowing for nonstationarity); more theory for irregularly spaced data; studying delicate problems where the rate of convergence depends on unknown parameters, such as in the notoriously difficult problem of autoregressive type processes with unit roots; improve the accuracy of distribution estimation by techniques such as Richardson extrapolation, and by optimal choice of block size; and pursue the development of goodness-of-fit tests in the dependent data case. These methods are especially useful in modelling of economic time series, due to the inherent difficulties caused by nonlinearity and nonstationarity. In part 2 of the proposal, the investigator will pursue the development of methods that have exact finite sample validity, such as the construction of conservative confidence regions, without the expense of losing efficiency, at least in large samples. Typical nonparametric methods are based on approximations or limit theorems, so that finite sample behavior is always an issue, and is often typically addressed by small scale simulations. In contrast, the goal here is to construct nonparametric procedures with guaranteed finite sample behavior and good efficiency.The statistical analysis of data is vital in many diverse scientific disciplines: physics, engineering, acoustics, geostatistics, medicine, econometrics, seismology, law, ecology, and others. The scope of modern statistical analysis is continually expanding, as is the need for inferential methods that are valid without imposing strong model assumptions. The investigator will continue the pursuit of the development of statistical methods that can be applied safely in practice, keeping in mind the many applications toward which such methods can fruitfully be applied. The philosophical approach of the investigator is to develop practical methods that have a robustness of validity so that they may be applied in increasingly complex situations. The impact of this work is potentially quite large because strong inferential statements can be made without imposing strong assumptions.