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I'd like a recent paper or book that shows in what conditions we can guarantee the existence of a minimal sufficient statistic.

I know the paper "Sufficiency and Statistical Decision Functions" (by R.R. Bahadur) and "Completeness, Similar Regions, and Unbiased Estimation: Part I" (by Lehmann and Scheffé). But these papers use weird notations and, therefore, are hard to understand. So I'd like a more recent paper or book about the existence of minimal sufficient statistics.

Thank you for your attention!

I know that there're statistical models that doesn't have minimal sufficient statistics, as you can see in the paper "Minimal Sufficient $\sigma$-Fields and Minimal Sufficient Statistics. Two Counterexamples".

What I want to know is some conditions that guarantee the existence of minimal sufficient statistics.

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  • $\begingroup$ As a useful start, Theorem 34.7 in Probability and Measure (3rd ed.) by Patrick Billingsley (it is not a recent book, though) states a sufficient condition for a minimal sub-$\sigma$-field to exist (which encompasses sufficient statistics as a special case). $\endgroup$
    – Zhanxiong
    Commented May 19 at 19:56

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