Microarrays are part of a new class of biotechnologies, which allow the monitoring of
expression levels of thousands of genes simultaneously. In microarray data analysis,
the comparison of gene expression profiles with respect to different conditions and
the selection of biologically interesting genes are crucial tasks. Multivariate
statistical methods have been applied to analyze these large data sets. To identify
genes with altered expression under two experimental conditions, we propose a
nonparametric statistical approach. Specifically, we propose estimating the
distributions of a t-type statistic and its null statistic, using kernel
methods. A comparison of these two distributions by means of a likelihood ratio test
can identify genes with significantly changed expressions. A new method to provide
more stable estimates of tail probabilities is proposed, as well as a method for the
calculation of the cut-off point and the acceptance region. The methodology is
applied to a leukaemia data set containing expression levels of 7129 genes, and is
compared with normal mixture model and the traditional t-test.
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