Mathematical Sciences: Inference for Nonlinear Time Series and Spatial Models

这一建议涉及的问题是， 非线性时间序列统计推断，状态空间 模型，随机场和空间点过程。 重点 将是非线性和非高斯模型。 一个统一的方法 将被用来研究渐近效率的性质， 估计器和测试。 局部渐近正态性为 研究了基于可能性的模型。 准- 可能性框架将用于以下情况： 可能性函数不可用。 经验贝叶斯方法将 也被调查。 统计分析和模型的研究 这一建议将对许多不同的 基础科学、工程学、健康科学、 经济和社会规划等。 统计数据，如 由于失业数字、各种经济指标、库存 市场波动、民意调查、货币汇率和 类似的都受到固有的随机变化， 可能是趋势。 这些涉及不确定性的方面， 有用地由适当的概率模型表示， 在这里提出的。 各种预测方法和 并会研究评估预测的准确性。 统计估计技术和检验方法 将研究所提出的模型的有效性。

This proposal is concerned with problems related to statistical inference in nonlinear time series, state-space models, random fields and spatial point processes. The emphasis will be on nonlinear and non-Gaussian models. A unified approach will be used to study the asymptotic efficiency properties of the estimators and tests. The local asymptotic normality will be investigated for the likelihood-based models. the quasi- likelihood framework will be used for the cases where the likelihood function is unavailable. Empirical Bayes methods will also be investigated. The statistical analysis and the models to be studied in this proposal will have an impact on a large number of diverse applications in Basic Sciences, Engineering, Health Sciences, Economic and Social Planning, among other. Statistical data such as the unemployment figures, various economic indicators, stock market fluctuations, opinion polls, currency exchange rates and the like are all subject to inherent random variations, and possibly trends. These aspects involving uncertainty can usefully be represented by appropriate probability models such as the ones proposed here. Various methods of forecasting and assessing the precision of the forecasts will also be studied. Techniques of statistical estimation and methods of testing the validity of the models proposed will be investigated.