  Controlling false discovery rate (FDR) is crucial for variable selection,
multiple testing, among other signal detection problems. In literature, there
is certainly no shortage of FDR control strategies when selecting individual
features, but the relevant works for structural change detection, such as
profile analysis for piecewise constant coefficients and integration analysis
with multiple data sources, are limited. In this paper, we propose a
generalized knockoff procedure (GKnockoff) for FDR control under such problem
settings. We prove that the GKnockoff possesses pairwise exchangeability, and
is capable of controlling the exact FDR under finite sample sizes. We further
explore GKnockoff under high dimensionality, by first introducing a new
screening method to filter the high-dimensional potential structural changes.
We adopt a data splitting technique to first reduce the dimensionality via
screening and then conduct GKnockoff on the refined selection set. Furthermore,
the powers of proposed methods are systematically studied. Numerical
comparisons with other methods show the superior performance of GKnockoff, in
terms of both FDR control and power. We also implement the proposed methods to
analyze a macroeconomic dataset for detecting changes of driven effects of
economic development on the secondary industry.
