  Information from various data sources is increasingly available nowadays.
However, some of the data sources may produce biased estimation due to commonly
encountered biased sampling, population heterogeneity, or model
misspecification. This calls for statistical methods to combine information in
the presence of biased sources. In this paper, a robust data fusion-extraction
method is proposed. The method can produce a consistent estimator of the
parameter of interest even if many of the data sources are biased. The proposed
estimator is easy to compute and only employs summary statistics, and hence can
be applied to many different fields, e.g. meta-analysis, Mendelian
randomisation and distributed system. Moreover, the proposed estimator is
asymptotically equivalent to the oracle estimator that only uses data from
unbiased sources under some mild conditions. Asymptotic normality of the
proposed estimator is also established. In contrast to the existing
meta-analysis methods, the theoretical properties are guaranteed even if both
the number of data sources and the dimension of the parameter diverge as the
sample size increases, which ensures the performance of the proposed method
over a wide range. The robustness and oracle property is also evaluated via
simulation studies. The proposed method is applied to a meta-analysis data set
to evaluate the surgical treatment for the moderate periodontal disease, and a
Mendelian randomization data set to study the risk factors of head and neck
cancer.
