Diagnostics in Statistical Methods for Multivariate Data including Longitudinal and Spatial Data

多元方法中基于影响函数和基于Cook局部影响的两种灵敏度分析方法之间的关系; 2）检测有影响的观测子集的方法; 3）空间数据分析中的灵敏度分析; 4）函数数据分析中的灵敏度分析; 5）多元方法中灵敏度分析统一统计软件的开发。对于第一个主题，我们证明了这两种方法在由（a）统计模型是否包含等式约束和（B）我们感兴趣的是所有参数还是参数子集定义的四种情况下的等价性，并在等价性的基础上，提出了主成分分析和典型成分分析中的局部影响分析方法，并研究了检测有影响力的观察子集的通用方法（[2]、[3]、[5]、[7]、[15]、[16]、[19]、[23]、TR [1]、TR、[2] ; [12]、[20]）。在第三个主题中，我们在空间数据分析的三个阶段中开发了SA，即，样本变异函数、变异函数模型估计和空间预测（[6]，[8]，[10]，[11]，[18]，[24]）。在函数数据分析中，我们研究了函数PCA中的SA（[17]，[22]）。第五个问题见[1]、[13]。

Relationship between the two approaches to sensitivity analysis (SA) in multivariate methods, one based on influence functions and the other based on the Cook's local influence, 2) Methodologies of detecting influential subsets of observations, 3) SA in spatial data analysis, 4) SA in functional data analysis, and 5) Development of unified statistical software of SA in various multivariate methods. For the first topic we proved the equivalence of both approaches in each of the four cases defined by (a) whether the statistical model contains any equality constraints and (b) whether we are interested in all parameters or a subset of parameters, and on the basis of the equivalence, we proposed methods of local influence analysis in principal component analysis and canonical component analysis, and also studied a general methodology for detecting influential subsets of observations ([2], [3], [5], [7], [15], [16], [19], [23], TR [1], TR,[2] ; [12], [20]). In the third topic we have developed SA in the three stages of spatial data analysis, i.e., sample variogram, variogram model estimation, and spatial prediction ([6], [8], [10], [11], [18], [24]). In functional data analysis we studied SA in functional PCA([17], [22]). For the fifth topic see [1], [13].