Mathematical Sciences: Measurement Error and Statistical Inference

本研究为测量数据的统计推断提供了新的方法 错误。这些方法利用高速计算的可用性， 模拟测量误差对数据集的影响。结果的 模拟实验形成了一种称为 模拟外推研究的第一个组成部分采用的方法 模拟外推估计的情况下， 对有误差测量的变量进行测量。第二 研究的一个组成部分使用复变量公式模拟 外推以绕过外推步骤。这是通过 使用复伪随机变量进行模拟实验， 计算感兴趣的参数的无偏估计方程。第三 研究的组成部分集中在两个样本的假设检验问题， 开发当一个样本的数据是渐近有效的测试， 测量误差。 数据中测量误差的存在会影响 从这些数据的统计分析得出的结论。比如说， 血压或胆固醇水平等风险因素的测量误差 影响了心脏病与这些疾病之间关系的统计学确定， 风险因素，通常导致低估的有益效果， 控制这些风险因素。类似地， 生态系统健康与生态系统压力源（污染物， 例如，由于无法准确测量应激源， 程度.这项研究发展了统计理论和方法， 从有误差的数据中推断出来。事实上， 测量发生在许多科学领域（调查方法，环境 研究，流行病学，医学例如）意味着研究广泛 适用因该研究使用新颖的计算机模拟方法来模拟 测量误差对数据集的影响以及对从 这样的数据。从模拟研究中获得的信息，然后用于 从数据中做出有效的推断，这些数据不受以下因素的偏见影响： 测量误差

This research develops new methods of statistical inference for data measured with error. The methods exploit the availability of high-speed computing to simulate the effects of measurement error on a data set. The results of such simulation experiments form the basis of a method of inference called simulation extrapolation. The first component of the research adapts the method of simulation extrapolation estimation to situations in which replicate measurements are made on the variables measured with error. The second component of the research uses the complex-variable formulation of simulation extrapolation to bypass the extrapolation step. This is accomplished by performing a simulation experiment using complex pseudo random variables to compute unbiased estimating equations for the parameters of interest. The third component of the research focuses on two-sample hypothesis testing problems, developing tests that are asymptotically valid when data from one sample are measured with error. The presence of measurement error in data can affect the validity of conclusions drawn from statistical analyses of such data. For example, measurement error in risk factors such as blood pressure or cholesterol level affects statistical determination of the relationship of heart disease to such risk factors, usually resulting in underestimation of the beneficial effects of controlling these risk factors. Similarly, statistical determination of the relationship of ecosystem health to ecosystem stressers (pollutants, for example) can be obscured by the inability to accurately measure stresser levels. This research develops statistical theory and methods for making valid inferences from data that are measured with error. The fact that errors of measurement occur in many areas of science (survey methodology, environmental studies, epidemiology, medicine for example) means that the research is widely applicable. The research uses novel computer simulation methods to simulate the effects of measurement error on a data set and on the conclusions drawn from such data. The information obtained from the simulation studies is then used to make valid inferences from the data that are free from the biasing effects of measurement error.