Topics in Statistical Modelling and Inference with High-Dimensional, Complex Data

技术正在改变我们的生活。数据现在以各种粒度大量收集。这些数据通常具有复杂的结构。能够捕捉这种复杂性的统计模型可以加深我们对数据生成机制的理解，并推动科学和工程领域的发展。然而，对这些数据进行建模可能具有挑战性，特别是当我们有内生测量值、离群值、缺失观测值或其他异常时。该研究计划的目标是解决在建模高维复杂数据时遇到的统计问题，特别关注时空，金融，商业智能，基因组数据。它将专注于开发强大的，计算上可行的和快速的模型选择程序，用于在候选模型集可能不包含真实模型的情况下，嘈杂的高维或超高维复杂数据。它将在一般模型公式中开发基于多个变点检测的两阶段正则化方法，例如，广义线性模型和函数数据模型，它们将同时估计所有变点并执行变量选择。它将处理高维回归模型中的多个变点检测，包括高维线性动态面板数据模型和时空回归模型。分别使用正则化方法和随机搜索方法，将进一步发展回归聚类。它将提出利用地理邻近信息的非静止时空建模。它将通过使用惩罚方法对网格数据进行有效分组，解决时空逆向建模问题。它将为海量的商业智能和基因组数据开发可行的关联规则挖掘。它将处理金融数据的统计建模问题，例如，长期隐含波动率和交易数据。对于我们提出的方法，我们将进行理论和方法研究;此外，我们将开发计算算法，以确保我们的方法在计算上是可行的和有效的，并从验证我们的研究结果的数值研究中提出结果。在拟议的研究中取得的进展将在统计建模，推理，计算及其在实践中的应用产生重大影响。

Technology is changing our lives. Data is now collected in large volumes at various granularities. Such data often exhibit complex structures. Statistical models able to capture this complexity can further our understanding of the underlying data-generating mechanism and advance relevant fields in science and engineering. However, modelling such data can be challenging, particularly when we have endogenous measurements, outliers, missing observations, or other anomalies.******The objective of this proposed research program is to tackle statistical problems encountered in modelling high-dimensional, complex data, with particular interest on spatio-temporal, financial, business intelligence, genomic data. It will focus on development of robust, computationally feasible and fast model selection procedures for noisy high- or ultra high-dimensional, complex data in the scenario that the set of candidate models may not contain the true one. It will develop a two-stage regularization method based multiple change-point detection in general model formulations, e.g., generalized linear models and functional data models, which will simultaneously estimate all the change-points and perform variable selection. It will deal with multiple change-point detection in high-dimensional regression models, which include high-dimensional linear dynamic panel data models and spatio-temporal regression models. It will further the development in regression clustering using respective regularization methods and stochastic search. It will propose non-stationary spatio-temporal modelling which leverage of geographical neighbourhood information. It will tackle spatio-temporal inverse modelling problems by effectively grouping grid data using penalized approaches. It will develop the feasible association rule mining for the massive business intelligence, and genomic data. It will address statistical modelling of financial data, e.g., long term implied volatility and trading data. For our proposed methods, we will carry out both theoretical and methodological investigations; in addition, we will develop computational algorithms to ensure that our methods are computationally feasible and efficient, and present results from numerical studies which validate our findings. The advancements achieved under the proposed research will produce significant impact in statistical modelling, inference, computing, and their applications in practice.