There is some frequentist procedure there, but it seems hard to not recognize the deep connection to Bayesian statistics and wonder if you should begin to quest

There is some frequentist procedure there, but it seems hard to not recognize the deep connection to Bayesian statistics and wonder if you should begin to question your baseline assumptions. Since the entire justification for using a shrinkage estimator has a whole lot more in common with the foundations of Bayesian statistics than it does with the foundations of frequentist stats. Purist frequentists using a shrinkage estimator looks a lot like heliocentric Ptolemic astronomy.