Ledoit and Wolf ("A Well-Conditioned Estimator for Large-Dimensional Covariance Matrices", 2004) proposed an estimator for the covariance matrix of a data set, $S^* = p I_d + (1 - p) \hat{S}$ with $p \in (0,1)$ (they gave a specific $p$ that I won't repeat), $I_d$ the identity matrix, and $\hat{S}$ the sample covariance matrix. I believe this is a fine estimator for uncorrelated data, and I want to use it for data that's potentially correlated. I like this specific approach since once one has $\hat{S}$ the adjustment is easy and fast to compute; for my purposes speed matters.

I want an estimator of this type when $\hat{S}$ is replaced with a kernel-based covariance matrix estimator, particularly the HAC estimators mentioned in the classic Andrews (1991) and Newey-West (1994) papers. Of course I could just take the HAC estimators and repeat the process for obtaining $p$ that Ledoit and Wolf suggested, but I would like theoretical justification for doing so. I've tried to use the Web of Science to find papers that cite both Ledoit-Wolf (2004) and either Andrews (1991) or Newey-West (1994) but I found nine papers doing so and I don't think any of them are talking about what I want to do.

Before declaring that there is no reference justifying replacing $\hat{S}$ with a different estimator, I would like to know if anyone here has a reference suggestion, or at least an argument for why what I want to do is theoretically justified.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.