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

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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].