  Selecting skilled mutual funds through the multiple testing framework has
received increasing attention from finance researchers and statisticians. The
intercept $\alpha$ of Carhart four-factor model is commonly used to measure the
true performance of mutual funds, and positive $\alpha$'s are considered as
skilled. We observe that the standardized OLS estimates of $\alpha$'s across
the funds possess strong dependence and nonnormality structures, indicating
that the conventional multiple testing methods are inadequate for selecting the
skilled funds. We start from a decision theoretic perspective, and propose an
optimal testing procedure to minimize a combination of false discovery rate and
false non-discovery rate. Our proposed testing procedure is constructed based
on the probability of each fund not being skilled conditional on the
information across all of the funds in our study. To model the distribution of
the information used for the testing procedure, we consider a mixture model
under dependence and propose a new method called "approximate empirical Bayes"
to fit the parameters. Empirical studies show that our selected skilled funds
have superior long-term and short-term performance, e.g., our selection
strongly outperforms the S\&P 500 index during the same period.
