In this thesis, we expand upon the work of Cui  and earlier authors by studying the problem of variable selection in a high-dimensional setting. Specifically, we consider a single vector X from a sequence model with noise components originating from a generalized normal distribution and determine the regions of exact and almost full selection with respect to a Hamming loss function. We make the routine assumption that the model studied is sparse. That is, the informative number of components is tiny in the model relative to the dimension d. An adaptive procedure is also proposed for estimating the signal components of X when the level of sparsity is unknown. A synthetic simulation and empirical study is then presented to showcase the aforementioned results. Lastly, we conclude the thesis by proposing areas of future work.