Mathematical Sciences: Problems in Mathematical Statistics

这项研究将由四名调查人员完成。第一个调查者将研究一类非参数变点估计的相合性、收敛速度、分布理论和有限样本性质。他还将研究从相依数据计算的退化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可信区间技术。第二个调查者将研究平滑方法、位置相关平滑、应用于模型选择、分类、带宽和核选择以及风险函数的平滑技术。第三个调查者将研究数据转换到正态或对称性和同方差的几个估计量，通过随机近似产生有效的非线性试验设计，并与第四个调查者一起研究非参数序贯年龄替代策略。最后一位研究人员将研究使用Ascombe-Colton模型进行序贯临床试验的战略实施，而不是标准的Neyman-Pearson模型。他还将继续研究最优停止问题的逼近方法，以及一些具有统计意义的布朗运动泛函的分布问题。

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.