Object data analysis has its origins in the development of directional data analysis, where many probability distributions were derived to generalize common univariate distributions to the unit circle. Many of these distributions were subsequently adapted for shape analysis, which gave rise to statistical methodologies for data on more general manifolds. However, parametric methods began to lose favor compared to nonparametric approaches in part because of a lack of general procedures for determining model adequacy on manifolds.
In this talk, we will present novel methodology for testing the plausibility that a data set is sampled from a hypothesized distribution against a general alternative. The procedure simulates data from the hypothesized distribution and then invokes the permutation principle to perform the test using the nearest neighbor graph of the combined data set. The resulting test statistic is distribution free. Examples will be provided for various types of object data.