Classical linear prediction methods based on least-square estimation yields radar images with high side lobes and many spurious scattering centers while singular value decomposition (SVD) truncation used to address these issues decreases the dynamic range of the image. So, radar images provided by these methods are not appropriate for classification purposes. In this work, sparsity constraints are induced on the prediction coefficients. The classification results demonstrate that the proposed sparse linear prediction methods give better accuracy rates compared to Multiple Signal Classification (MUSIC) method conventionally used for limited bandwidth-observation angle data. Classification performances of proposed methods are also investigated in case of the missing backscattered data. It is shown that the proposed methods are not affected from the missing data unlike the MUSIC method whose performance decreases with the increase in the percentage of the missing data.