"But with frequentist methods it's not even clear what kind of assumptions you're making."
I don't understand what you mean by this.
For a simple, concrete example: take the problem of fitting a distribution to a sample of real random variables. It seems that a Frequentist would make the following assumptions:
1. The data comes iid from some unknown but fixed distribution.
2. This true distribution is included within some set of distributions: eg, the set of normal distributions with real mean and non-negative real variance.
They would then use some estimator to estimate the parameters. The choice of estimator is perhaps justified by some theoretical properties, eg, consistency etc. This gives another assumption.
3. The best estimator to use is the one which is optimal with regard to properties x,y,z.
If it is not clear what assumptions I am making and I have explicitly stated some, presumably there are others which I have left unstated. Could you explain why you think the above collection is insufficient?
I don't understand what you mean by this.
For a simple, concrete example: take the problem of fitting a distribution to a sample of real random variables. It seems that a Frequentist would make the following assumptions:
1. The data comes iid from some unknown but fixed distribution.
2. This true distribution is included within some set of distributions: eg, the set of normal distributions with real mean and non-negative real variance.
They would then use some estimator to estimate the parameters. The choice of estimator is perhaps justified by some theoretical properties, eg, consistency etc. This gives another assumption.
3. The best estimator to use is the one which is optimal with regard to properties x,y,z.
If it is not clear what assumptions I am making and I have explicitly stated some, presumably there are others which I have left unstated. Could you explain why you think the above collection is insufficient?