I'm looking to learn about the main/popular alternatives when it comes to estimating correlations that I've missed in the following list. The best answer will provide a reference (can be Wikipedia), a quick description and a motivation/purpose/reason to use.

Here's the ones that I'm already aware of:

$$\text{Unconditional estimators}$$

$$\text{Time-varying estimators}$$

  • DCC-fGARCH time-varying correlation estimate. (i.e., DCC(p,q) with different GARCH variants; common ones in finance are GARCH, eGARCH, TGARCH or GJR-GARCH).

  • Time-varying correlations by Kalman Filter regressions (however I'm ignorant of this methodology, I've just seen it in a paper that I glanced through).

$$\text{Estimators for distributional extremes}$$

  • The new technology on the block; quantile correlations, a purportedly robust way of estimating the correlations at the extremes/tails of one of the variables.

I know that some correlation work has been done with random matrices but I'm ignorant of this.

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    $\begingroup$ It's not really possible to list all correlation estimates. There's potentially an infinity of infinities of them. $\endgroup$ – Glen_b Dec 14 '12 at 9:51
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    $\begingroup$ Do you care about the measures of association in contingency tables? $\endgroup$ – Glen_b Dec 14 '12 at 9:55

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