Mining for Low-abundance Transcripts in Microarray Data
by
Yi Lin (Statistics),
Samuel T. Nadler (Biochemistry),
Alan D. Attie (Biochemistry) and
Brian S. Yandell
(Statistics & Horticulture)
Technical Report #1031, January 2001,
U WI Madison Statistics
Plant and animal studies of quantitative trait loci provide data which
arise from mixtures of distributions with known mixing proportions.
Previous approaches to estimation involve modelling the distributions
parametrically. We propose a semiparametric alternative which assumes
that the log ratio of the component densities satisfies a linear model,
with the baseline density unspecified. It is demonstrated that a
constrained empirical likelihood has an irregularity under the null
hypothesis that the two densities are equal. A factorization of the
likelihood suggests a partial empirical likelihood which permits
unconstrained estimation of the parameters. The partial likelihood is
shown to give consistent and asymptotically normal estimators,
regardless of the null. The asymptotic null distribution of the
log-partial likelihood ratio is chi-square. Theoretical calculations
show that the procedure may be as efficient as the full empirical
likelihood in the regular set-up. The usefulness of the robust methodology
is illustrated with a rat study of breast cancer resistance genes.
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