  We consider the problem of identifying the support of the block signal in a
sequence when both the length and the location of the block signal are unknown.
The multivariate version of this problem is also considered, in which we try to
identify the support of the rectangular signal in the hyper- rectangle. We
allow the length of the block signal to grow polynomially with the length of
the sequence, which greatly generalizes the previous results in [16]. A
statistical boundary above which the identification is possible is presented
and an asymptotically optimal and computationally efficient procedure is
proposed under Gaussian white noise in both the univariate and multivariate
settings. The problem of block signal identification is shown to have the same
statistical difficulty as the corresponding problem of detection in both the
univariate and multivariate cases, in the sense that whenever we can detect the
signal, we can identify the support of the signal. Some generalizations are
also considered here: (1) We ex- tend our theory to the case of multiple block
signals. (2) We also discuss about the robust identification problem when the
noise distribution is un- specified and the block signal identification problem
under the exponential family setting.
