Mathematical Sciences: Problems in Mathematical Statistics

这项研究将由四位研究者完成。第一个研究者将研究一类非参数变点估计的一致性、收敛率、分布理论和有限样本性质。他还将研究由相关数据计算的退化u统计量的渐近分布理论，并比较三种基于平稳序列的一般统计量的子序列值的非参数置信区间技术。第二个研究者将研究平滑方法的各个方面，位置依赖平滑，应用于模型选择的平滑技术，分类，带宽和核选择以及危险函数。第三位研究者将研究数据转换为正态或对称和均方差的几种估计，通过随机近似生成有效的非线性实验设计，并与第四位研究者共同研究非参数顺序年龄替代政策。最后一名研究者将研究使用Ascombe-Colton模型进行顺序临床试验的战略意义，而不是标准的Neyman-Pearson模型。他还将继续研究最优停止问题的近似方法和一些布朗运动泛函的分布问题，这是统计上的兴趣。

This research will be done by four investigators. The first investigator will study the consistency, rates of convergence, distribution theory and finite-sample properties of a class of nonparametric change-point estimators. He will also investigate the asymptotic distribution theory of degenerate U-statistics computed from dependent data and compare three nonparametric confidence interval techniques which are based upon subseries values of a general statistics from a stationary sequence. The second investigator will study aspects of smoothing methods, location dependent smoothing, smoothing techniques applied to model selection, classification, bandwidth and kernel selection and hazard functions. The third investigator will study several estimators of data transformation to normality or to symmetry and homoscedasticity, generation of efficient nonlinear experimental design by stochastic approximation and jointly with the fourth investigator, he will look at nonparametric sequential age replacement policies. The last investigator will study the strategic implecations of using the Ascombe-Colton model for sequential clinical trials, as apposed to the standard Neyman-Pearson model. He will also continue to study approximation methods for optimal stopping problemsand distributional questions for some functionals of Brownian motion, of statistical interest.