U.S.-Czech Mathematics Research on Robust Statistical Inference Based on Second Order Asymptotic Relations

INT 9600518 Sen 查佩尔山的北卡罗来纳州大学的Pranab Sen博士和布拉格的查尔斯大学的Jana Jurechova博士之间的这个美国-捷克数学项目将研究线性模型和更复杂背景下（如纵向数据模型）稳健统计过程的高阶渐近性质。 研究人员打算利用他们在非参数方法和渐近理论方面的经验来完善几个相关领域的程序：1）线性模型中的k步M估计; 2）回归参数的二阶稳健估计; 3）r估计量和回归秩分数估计量之间的关系;以及4）统计泛函的二阶表示。 结果预计将导致选择的估计的基础上计算的复杂性，这将是有用的情况下，样本是中等大小。 研究人员希望将他们的发现应用于新的统计程序的开发，特别强调假设检验和生物医学和环境应用中出现的非标准模型。 该项目是统计和概率，通过使美国和东欧的专家能够联合收割机互补人才并在共同感兴趣和能力强的领域共享研究资源，实现了推进科学知识的计划目标。 ??

INT 9600518 Sen This U.S-Czech mathematics project between Dr. Pranab Sen of the University of North Carolina, Chapel Hill, and Dr. Jana Jurechova of Charles University, Prague, will examine higher-order asymptotic properties of robust statistical procedures in the linear model and in more sophisticated contexts, such as models for longitudinal data. The researchers intend to build upon their experience in nonparametric methods and asymptotic theory to refine procedures for several related areas: 1) k-step M-estimation in linear models; 2) second order robust estimation of regression parameters; 3) relations between r-estimators and regression rank scores estimators; and 4)second order representations for statistical functionals. Results are expected to lead to choices of estimators based on computational complexities that will be useful in situations when samples are of moderate size. The researchers expect to apply their findings in the development of new statistical procedures with special emphasis on tests of hypotheses and on non-standard models that arise in biomedical and environmental applications. This project is statistics and probability fulfills the program objective of advancing scientific knowledge by enabling experts in the Unites States and Eastern Europe to combine complementary talents and share research resources in areas of strong mutual interest and competence. ??