New Approaches to Nonparametric Regression Estimation for Continuous and Discrete Time Series

连续和离散时间序列非参数回归估计的新方法

• 批准号: 9703876
• 负责人: Elias Masry
• 金额: $ 16.2万
• 依托单位: University of California-San Diego
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-07-01 至 2001-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9703876&HistoricalAwards=false
• 关键词: New; Approaches; Nonparametric; Regression; Estimation

Masry 9703876 The research is concerned with regression functions estimation in a hybrid setting: the underlying processes are continuous in time, and so is the regression function, but the observations are taken at discrete-times. This is common in many practical situations where the collected data is irregularly spaced as in environmental and oceanographic studies. The instants at which the data is obtained constitute a point process with a FINITE mean sampling rate but nevertheless result in no loss of information. The goal of the research is to identify appropriate non-equally spaced sampling schemes; formulate suitable estimates based on a modified Nadaraya-Watson approach and on the more recent local polynomial fitting approach; and study their convergence properties including asymptotic normality and rates of strong convergence. A fundamental requirement is that the consistency of the regression estimates, as the number of observations tends to infinity, holds for ALL positive values of the mean sampling rate. Results of this type do not hold for conventional equally-spaced data unless the sampling rate is allowed to diverge to infinity. Scientists and engineers collect huge amounts of data in wide range of disciplines including communication systems (e.g., Internet traffic, satellites), econometrics (e.g. stock market), geology (e.g. earthquakes), and environmental science (e.g. pollution levels). While much of the observed data is continuous in time, the processing of the data is carried out by using computers which convert the data to a digital form. The research develops digital processing methodologies (irregular sampling methodologies) which do not lose any information during the conversion process from continuous-time data to discrete-time data. The context of the research is 1) to forecast the future evolution of the phenomena being observed and 2) to filter signals observed in the presence of corrupting noise.

Masry 9703876 该研究关注的是回归函数估计在一个混合设置：基本过程是连续的时间，所以是回归函数，但观察是在离散时间。 这在许多实际情况下是常见的，如在环境和海洋学研究中收集的数据是不规则间隔的。 获得数据的时刻构成具有有限平均采样率的点过程，但不会导致信息丢失。 研究的目标是确定适当的非等间距抽样方案，制定适当的估计修改后的Nadaraya-Watson方法和最近的局部多项式拟合方法的基础上，并研究其收敛特性，包括渐近正态性和强收敛率。一个基本要求是回归估计的一致性，因为观测值的数量趋于无穷大，对平均采样率的所有正值都成立。这种类型的结果不适用于传统的等距数据，除非采样率允许发散到无穷大。 科学家和工程师收集大量的数据，在广泛的学科，包括 通信系统（例如，互联网流量、卫星）、计量经济学（如股票市场）、地质学（如地震）和环境科学（如污染水平）。虽然许多观测数据在时间上是连续的，但数据的处理是通过使用计算机将数据转换为数字形式来进行的。该研究开发了数字处理方法（不规则采样方法），这些方法在从连续时间数据到离散时间数据的转换过程中不会丢失任何信息。研究的背景是：1）预测所观察到的现象的未来演变; 2）过滤在存在破坏性噪声的情况下观察到的信号。