Title: High-dimensional statistical analysis: Spiked models and data transformation
Authors: Makoto Aoshima - University of Tsukuba (Japan) [presenting]
Abstract: Any high-dimensional data is classified into two disjoint models: the strongly spiked eigenvalue (SSE) model and the non-SSE (NSSE) model. In actual high-dimensional data, a non-sparse and low-rank structure which contains strongly spiked eigenvalues is often found; a structure which fits the SSE model. Under the SSE model, it may be noted that the asymptotic normality of high-dimensional statistics is not valid because it is heavily influenced by strongly spiked eigenvalues. To enable a unified treatment of both the SSE models and non-SSE models, data transformation techniques that transform the SSE models to the non-SSE models were developed previously. Following this novel methodology, strongly spiked eigenvalues are accurately detected by using new PCA-type techniques. With the transformed data, one can create a new statistic which can ensure high accuracy for inferences by using asymptotic normality even under the SSE models. The new techniques to handle high-dimensional data will be demonstrated to solve two-sample problems and classification problems.