Nonparametric estimation, bayesian statistics and MCMC

非参数估计、贝叶斯统计和 MCMC

• 批准号: 36527-2007
• 负责人: Perron, François
• 金额: $ 1.24万
• 依托单位: Université de Montréal
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2007
• 资助国家: 加拿大
• 起止时间: 2007-01-01 至 2008-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=365379
• 关键词: Nonparametric; estimation; bayesian; statistics; MCMC

The project has three themes.1)  In dimension 2 a random the distribution function of a vector (X,Y) can be represented by the marginal distribution of X and Y and the copula which gives a description on how X and Y interact with each other.  For the extrems value distributions the copula depends on a special function A called the Pickands dependance function.  Moreover A is convex ad satisfies the following condition, max(u,1-u)< A(u) < 1 for all u in (0,1).  I want to estimate A with a bayesian approach in a nonparametric setting.2)  I am interested in the problem of estimating a cdf and also a pdf using a nonparametric approach.  I want to develop estimators which take into account a prior information.  These estimators need to be robust if the prior information is not supported by the sample and they have to be smooth.3)  In many cases, it cost almost nothing to rank observations in a large sample but it is expensive to make measurements.  In this situation ranked set sampling is an approachwhere you make measurements on some specific order statistics instead of sampling randomly.  For the estimation of the mean ranked set sampling reduces the variance of the estimator.  I want to improve on ranked set sampling.

本课题主要有三个方面的内容：1）在二维随机空间中，向量（X，Y）的分布函数可以用X和Y的边际分布以及描述X和Y相互作用的Copula来表示，对于极值分布，Copula依赖于一个特殊的函数A，称为Pickands依赖函数，并且A是凸的，满足以下条件，max（u，1-u）< A（u）< 1对于（0，1）.我想在非参数设置下用baidu方法估计A。2）我对使用非参数方法估计cdf和pdf的问题感兴趣。我想开发考虑先验信息的估计器。如果先验信息不支持，这些估计器需要是鲁棒的。样品，他们必须是光滑的。3）在许多情况下，在大样本中对观测值进行排序几乎没有任何成本，但进行测量是昂贵的。在这种情况下，排序集抽样是一种对某些特定顺序统计量进行测量的方法，而不是随机抽样。对于均值的估计，排序集抽样减少了估计量的方差。我想改进秩集抽样