2 problems
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The conjecture that the sieve estimator equals Grenander's estimator
Sieve–Grenander conjecture. The sieve estimator above is the same as Grenander's estimator. Consequently, the clinical version of the empirical-prior model is covered by the stated…
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Wellner's conjecture on the limiting variance of the Grenander estimator's Hellinger loss
Wellner's conjecture. The limiting variance in the central limit theorem for the Hellinger loss of Grenander's estimator does not depend on the underlying monotone density…