报告题目：Nonparametric estimation of probability density functions for irregularly observed spatial data

时 间： 2014年7月15日上午10:00

地 点： 数学学科楼三楼310报告厅

报 告 人： 卢祖帝 教授 （Prof. Zudi Lu）

报告人简介：卢祖帝（Zudi Lu），现为英国南安普顿大学统计科学研究所（s3ri）和数学科学学院统计学讲座教授，国际统计学会(International Statistical Institute)当选会员，澳大利亚国家研究基金会（Australian Research Council）2010年度杰出青年基金(Future Fellowships Grant)获得者。1996年获中国科学院概率统计博士学位后，曾在中国科学院数学与系统科学研究院（1997-2003年）以及多个国际著名大学工作，包括比利时新鲁汶大学（1996-1997年），英国伦敦经济学院（2003-2006年），澳大利亚阿得莱德大学（2009-2013）和科廷大学（2006-2009）等。研究方向包括：非线性金融时间序列模型和金融统计；非线性时空模型的统计推断和计算；非参数/半参数模型统计推断；统计学习；医学统计；贝叶斯统计等。担任顶级杂志Journal of Time Series Analysis的副主编和Cogent Mathematics杂志统计部分的主编(section editor)。在统计学年鉴（Annals of Statistics），英国皇家统计学会杂志（Journal of the Royal Statistical Society Series B）,经济理论（Econometric Theorey）,伯努利（Bernoulli）等世界顶级学术期刊发表论文50余篇。

报告摘要： Nonparametric estimation of probability density functions, both marginal and joint densities, is a very useful tool in statistics. The kernel method is popular and applicable to dependent data, including time series and spatial data. But at least for the joint density, one has had to assume that data are observed at regular time intervals or on a regular grid in space. Though this is not very restrictive in the time series case, it often is in the spatial case. In fact, to a large degree it has precluded applications of nonparametric methods to spatial data because such data often are irregularly positioned over space. In this paper, we propose nonparametric kernel estimators for both the marginal and in particular the joint probability density functions for non-gridded spatial data. Large sample distributions of the proposed estimators are established under mild conditions, and a new framework of expanding-domain infill asymptotics is suggested to overcome the shortcomings of spatial asymptotics in the existing literature. A practical, reasonable selection of the bandwidths on the basis of cross- validation is also proposed. We demonstrate by both simulations and real data examples of moderate sample size that the proposed methodology is effective and useful in uncovering nonlinear spatial dependence for general, including non-Gaussian, distributions.

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2014年7月14日