# What are some well-known unbiased estimator of regression coefficient besides OLS estimator?

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)?

• 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
– Ben
May 13 at 0:47
• 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
– Ben
May 13 at 0:53
• The title does not seem to quite match the question; consider updating. May 13 at 9:47