39,070 research outputs found
Comparing large covariance matrices under weak conditions on the dependence structure and its application to gene clustering
Comparing large covariance matrices has important applications in modern
genomics, where scientists are often interested in understanding whether
relationships (e.g., dependencies or co-regulations) among a large number of
genes vary between different biological states. We propose a computationally
fast procedure for testing the equality of two large covariance matrices when
the dimensions of the covariance matrices are much larger than the sample
sizes. A distinguishing feature of the new procedure is that it imposes no
structural assumptions on the unknown covariance matrices. Hence the test is
robust with respect to various complex dependence structures that frequently
arise in genomics. We prove that the proposed procedure is asymptotically valid
under weak moment conditions. As an interesting application, we derive a new
gene clustering algorithm which shares the same nice property of avoiding
restrictive structural assumptions for high-dimensional genomics data. Using an
asthma gene expression dataset, we illustrate how the new test helps compare
the covariance matrices of the genes across different gene sets/pathways
between the disease group and the control group, and how the gene clustering
algorithm provides new insights on the way gene clustering patterns differ
between the two groups. The proposed methods have been implemented in an
R-package HDtest and is available on CRAN.Comment: The original title dated back to May 2015 is "Bootstrap Tests on High
Dimensional Covariance Matrices with Applications to Understanding Gene
Clustering
Simulation-Based Hypothesis Testing of High Dimensional Means Under Covariance Heterogeneity
In this paper, we study the problem of testing the mean vectors of high
dimensional data in both one-sample and two-sample cases. The proposed testing
procedures employ maximum-type statistics and the parametric bootstrap
techniques to compute the critical values. Different from the existing tests
that heavily rely on the structural conditions on the unknown covariance
matrices, the proposed tests allow general covariance structures of the data
and therefore enjoy wide scope of applicability in practice. To enhance powers
of the tests against sparse alternatives, we further propose two-step
procedures with a preliminary feature screening step. Theoretical properties of
the proposed tests are investigated. Through extensive numerical experiments on
synthetic datasets and an human acute lymphoblastic leukemia gene expression
dataset, we illustrate the performance of the new tests and how they may
provide assistance on detecting disease-associated gene-sets. The proposed
methods have been implemented in an R-package HDtest and are available on CRAN.Comment: 34 pages, 10 figures; Accepted for biometric
Trade, Capital Redistribution and Firm Structure
A model of heterogeneous firms with multiple products and two production factors (labor and capital) is used to study how trade liberalization affects firms’choices through both product and factor markets. Trade liberalization is shown to always redistribute capital toward more efficient firms and always to improve an industry’s total factor productivity. However, it may reduce capital prices and cause labor productivity to drop. Low efficiency firms are affected mainly by changes in the factor market, while high efficiency firms are affected mainly by changes in the product market. In response to trade liberalization, low efficiency firms always reduce their product scope, but high efficiency firms may expand their scope. The model demonstrates the importance of the interplay between product and factor markets.firm heterogeneity, trade liberalization, multiproduct, multifactor, firm structure, scale, scope, mergers and acquisitions
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