Curve Estimation Involving Time Series

DMS 9625412 Efromovich 本文对曲线估计的研究主要集中在最优估计上， 自适应非参数时间序列估计是：（i）渐近 有效的不同损失函数，（ii）良好的执行情况下， 与基于基础的同行预言机相比， 曲线，（iii）有效地压缩数据，以解决 环境问题，如监测水质或分析 通过海洋磁异常的全球变化;（iv）对噪声分布的鲁棒性 和长协方差观测。渐近分析是基于对 局部经验过程，混合序列的现代概率结果 和频谱密度的精确数据驱动估计器。数据驱动估计器 对于小样本量的情况下，从理论上通过 甲骨文不等式和数值通过密集的蒙特卡罗研究。 %%% 该研究涉及开发最佳方法， 图像的恢复出现在不同的科学问题，包括： (i)激素的分泌，如胰岛素分泌， 到目前为止，由于噪声、长期依赖性 （二）监测水质; 分析大型，相关和稀疏的数据集， 高效、计算密集型数据压缩; (iii)地质事件的时间，包括板块运动和气候变化 变化;（iv）测试和模拟新材料的特性。 ***

DMS 9625412 Efromovich This research on curve estimation focuses on optimal adaptive nonparametric time series estimators that are: (i) asymptotically efficient for different loss functions, (ii) well performing for the case of small sample sizes in comparison with peer oracles based on underlying curve, (iii) efficiently data-compressing for problems arising in environmental problems like monitoring quality of water or the analysis of global change via marine magnetic anomaly; (iv) robust to distribution of noise and long covariance observations. The asymptotic analysis is based on the study of local empirical processes, modern probabilistic results for mixing sequences and sharp data-driven estimators of spectral density. Data-driven estimators for the case of small sample sizes are explored both theoretically via oracle inequalities and numerically via intensive Monte Carlo study. %%% The research involves the development of optimal methods for the recovery of images that arise in different scientific problems including: (i) secretion of hormones such as insulin secretion where no other methods have been successful so far due to noisy, long-dependent and indirect data; (ii) monitoring quality of water based on the analysis of large, correlated and sparse data sets that have undergone efficient, computationally intensive data-compression; (iii) timing of geological events, including plate motions and climatological variations; (iv) testing and modeling properties of new materials. ***