Publications (4)0 Total impact
ABSTRACT: This paper considers the asymptotic power of likelihood ratio test (LRT) for
the identity test when the dimension p is large compared to the sample size n.
The asymptotic distribution of LRT under alternatives is given and an explicit
expression of the power is derived. A simulation study is carried out to
compare LRT with other tests. All these studies show that LRT is a powerful
test to detect eigenvalues around zero.
Key words and phrases: Covariance matrix, High dimensional data, Identity
test, Likelihood ratio test, Power
ABSTRACT: In this work, a new data-driven shrinkage estimator for the population
precision matrix has been introduced using random matrix theory. The new
estimation is non-parametric without assuming a specific parameter distribution
for the data and also there is no prior information about the structure of the
population covariance matrix. We demonstrate by both theoretical and empirical
studies that the new estimator, which is applicable for p > n, has good
properties for a wide range of dimensions and sample sizes. Moreover, even if p
< n, our new method always dominates the inverse sample covariance matrix and
performs comparably with existing methods.
ABSTRACT: In this paper, a shrinkage estimator for the population mean is proposed
under arbitrary quadratic loss functions with unknown covariance matrices. The
new estimator is non-parametric in the sense that it does not assume a specific
parametric distribution for the data and it does not require the prior
information on the population covariance matrix. Analytical results on the
improvement of the proposed shrinkage estimator are provided and some
corresponding asymptotic properties are also derived. Finally, we demonstrate
the practical improvement of the proposed method over existing methods through
extensive simulation studies and real data analysis. Keywords: High-dimensional
data; Shrinkage estimator; Large $p$ small $n$; $U$-statistic.
ABSTRACT: This work studies the theoretical rules of feature selection in linear
discriminant analysis (LDA), and a new feature selection method is proposed for
sparse linear discriminant analysis. An $l_1$ minimization method is used to
select the important features from which the LDA will be constructed. The
asymptotic results of this proposed two-stage LDA (TLDA) are studied,
demonstrating that TLDA is an optimal classification rule whose convergence
rate is the best compared to existing methods. The experiments on simulated and
real datasets are consistent with the theoretical results and show that TLDA
performs favorably in comparison with current methods. Overall, TLDA uses a
lower minimum number of features or genes than other approaches to achieve a
better result with a reduced misclassification rate.