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We consider the problem of identifying the support of the block signal in asequence 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 toidentify the support of the rectangular signal in the hyper- rectangle. Weallow the length of the block signal to grow polynomially with the length ofthe sequence, which greatly generalizes the previous results in [16]. Astatistical boundary above which the identification is possible is presentedand an asymptotically optimal and computationally efficient procedure isproposed under Gaussian white noise in both the univariate and multivariatesettings. The problem of block signal identification is shown to have the samestatistical difficulty as the corresponding problem of detection in both theunivariate and multivariate cases, in the sense that whenever we can detect thesignal, we can identify the support of the signal. Some generalizations arealso considered here: (1) We ex- tend our theory to the case of multiple blocksignals. (2) We also discuss about the robust identification problem when thenoise distribution is un- specified and the block signal identification problemunder the exponential family setting.

Identifying the Support of Rectangular Signals in Gaussian Noise