Is there any other unbiased estimator of regression coefficient than OLS? For instance, one might consider using unbiased estimator with less computational cost (since OLS involves matrix inversion)?
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2$\begingroup$ This is an interesting question! I take it we can assume that the sample size ($n$) is larger than the number of features ($p$)? Also, just to stress: matrix inversion is not required to find the OLS estimates. Only solving a linear system is required $\endgroup$– BenMay 13 at 0:47
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$\begingroup$ Special case 1: If the design matrix $X \in \mathbb{R}^{n \times p}$ is orthogonal, then OLS can be calculated in $2np$ flops, which will is hard to beat. Special case 2: if $X$ is the identity, the response vector itself is an unbiased estimator, which can be computed in $0$ flops. Perhaps there's more gains for less structured design matrices, though $\endgroup$– BenMay 13 at 0:53
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$\begingroup$ The title does not seem to quite match the question; consider updating. $\endgroup$– Richard HardyMay 13 at 9:47
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