Negatively correlated estimators for the AR-1 process

I have the following question. Assume we have a stochastic process

begin{equation}
y_t = gamma + phi y_{t-1} + epsilon_t, epsilon_t sim mathcal{N}(0, sigma^2),
end{equation}

where $|phi| < 1$ – stationary process. My main goal is to estimate the $phi$. In my context, I care more about unbiasedness rather consistency of the estimator. I’m trying several estimators (I provide them just for the example, the exact definition isn’t necessary and could be found for example here http://wojtek.zielinski.statystyka.info/Moj_ojciec/public_html/Preprint726.pdf):

• OLS;
• MLE;
• Burg’s estimator;
• M-estimator with Huber loss function;
• Hurwicz estimator;

When I simulate the datasets to estimate the sampling distribution of the estimators it appears that all of them are positively correlated, which is reasonable. If we have an accidental large drop in the time series all estimators will favor a higher $phi$ than a smaller. The next step I want to combine all the estimators in one.

My question is the following, could we find the estimator which will negatively correlate to the rest. By finding such we can greatly reduce the sampling variance of the combined estimator and hence the confidence intervals or if it’s not possible how could we precisely state that all estimators should positively correlate.