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.