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In this paper, we investigate a recently proposed efficient subspace learning method, Spectral Regression Discriminant Analysis (SRDA), and its kernel version SRKDA for head pose estimation. One important unsolved issue of SRDA is how to automatically determine an appropriate regularization parameter. The parameter, which was empirically set in the existing work, has great impact on its performance. By formulating it as a constrained optimization problem, we present a method to estimate the optimal regularization parameter in SRDA and SRKDA. Our experiments on two databases illustrate that SRDA, especially SRKDA, is promising for head pose estimation. Moreover, our approach for estimating the regularization parameter is shown to be effective in head pose estimation and face recognition experiments.