On Dimensionality of Mean Structure
from a Single Data Matrix
We consider inference from data matrices
that have low dimensional mean structures. In educational testing and in
probe-level microarray data, estimation and inference are often made from a
single data matrix believed to have a uni-dimensional mean structure. In this
talk, we focus on probe-level microarray data to examine the adequacy of a
uni-dimensional summary for characterizing the data matrix of each probe-set.
To do so, we propose a low-rank matrix model, and develop a useful framework
for testing the adequacy of uni-dimensionality against targeted alternatives.
We analyze the asymptotic properties of the proposed test statistics as the
number of rows (or columns) of the data matrix tends to infinity, and use Monte
Carlo simulations to assess their small sample performance. Applications of the
proposed tests to GeneChip data show that evidence against a uni-dimensional
model is often indicative of practically relevant features of a probe-set.
The talk is based on
joint work with Xingdong Feng, currently a postdoctoral fellow at the National
Institute of Statistics Sciences.