Estimating the Null and the Proportion of non-Null Effects in Large-Scale Multiple Comparisons
Jiashun Jin and Tony Cai
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Abstract:
An important issue raised by Efron (2004) in the context of
large-scale multiple comparisons is that in many
applications the usual assumption that the null distribution is known
is incorrect, and seemingly negligible differences in the null may
result in large differences in subsequent studies. This suggests that
a careful study of estimation of the null is indispensable.
In this paper, we consider the problem of estimating a null normal distribution, and a closely related problem, estimation of the proportion of non-null effects. We develop an approach based on the empirical characteristic function and Fourier analysis. The estimators are shown to be uniformly consistent over a wide class of parameters. Numerical performance of the estimators is investigated using both simulated and real data. In particular, we apply our procedure to the analysis of breast cancer and HIV microarray data sets. The estimators perform favorably in comparison to existing methods.
- Paper:
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