Estimate a sufficient statistic for a distribution.
Free CAS MAS-I (Modern Actuarial Statistics I) lesson in Statistics. 8 min read, ~1,243 words.
Fisher-Neyman factorization: is sufficient for iff the joint density factors as, where does not depend on. Exponential family rule: if, then is sufficient. One-parameter benchmarks: for Bernoulli, Poisson, Exponential, Geometric, and Normal( known); for Uniform(0, ). Two-parameter benchmarks: for Normal; for Uniform( ); for Gamma. Rao-Blackwell + Lehmann-Scheffé: conditioning an...
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What this lesson covers
- Content
- Example 1
- Example 2
- Common Mistakes
- Key Takeaways
- Exam Shortcuts
Learning objectives
- B2
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