Data Driven Convergence in Statistical Estimators
summary
Gives a precise, provable criterion for when a pointwise-consistent estimator can also produce a universal, data-driven stopping rule that reliably signals accuracy: a class is insurable iff every distribution has a nonzero neighborhood where the target property is trivial (tight for percentile bounds, strongly compressible for redundancy). Shows a negative example—hiding of entropy—where tiny ε and huge support m make the all-zero sample look ambiguous, and uses the Lindelöf property of countable alphabets to construct the stopping scheme and cover the class. Compares where prediction and compression diverge.
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chapters (9)
- 0:00Problem statement
- 1:44Defining estimation goals
- 3:58Asymptotics and consistency
- 6:52Local property focus
- 9:20Example: hiding entropy
- 13:41Insurability concept
- 17:11Stopping rules and neighborhoods
- 21:02General characterization
- 25:00Applications and conclusion
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