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Given any model for the underlying probability distribution $f(\theta)$, sufficient statistics provides us a way to estimate the model parameter $\theta$ with confidence without wasting the sample observation.

My question is that in my problem, I don't know which $f(\theta)$ or $g(\phi)$ and so on, is the right model of my underlying dataset. In such a scenario, how should I choose the appropriate model as well as the model parameter?

Should I first perform hypothesis testing to find the correct model and then learn the model parameters or is there some way to do this simultaneously. I would appreciate if someone could share their thoughts or guide me to the resource that may help me in understanding the underlying issue.

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    $\begingroup$ It's an excellent question - one with implications for a large amount of statistical inferential modelling (since much of it is predicated on just such conditioning on an assumed distributional model). $\endgroup$ – Glen_b Sep 11 '18 at 21:48
  • $\begingroup$ Sufficiency is conditional on the model (or on a collection of models), hence should not be of much use for model comparison, in general. $\endgroup$ – Xi'an Sep 16 '18 at 10:20

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