4 problems

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Adaptive minimax optimality conjecture for the SOLIT rule
Adaptive minimax optimality conjecture. The convergence rate of the SOLIT rule should be adaptively minimax optimal over the whole range of smoothness classes specified by the inde…
Conjectureopenadaptive-estimation minimax-theory statistical-inverse-problemsarXiv posted 2 days ago
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Near-rate-optimality of the Smoluchowski displacement distribution estimator
Let $F(x_0)$ be the distribution function of particle displacement evaluated at $x_0$ , and let $\hat{F}_{h_*}(x_0)$ be the estimator with the bandwidth $h_*$ used in the preceding…
Conjectureopennonparametric-estimation smoluchowski-processes statistical-inverse-problemsarXiv posted 2 days ago
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Nickl–Reiß conjecture on a Donsker theorem for discretely observed compound Poisson processes
Nickl–Reiß conjecture. In this discretely observed setting, it should be possible to develop a result similar to Donsker's theorem for inference on the jump distribution $F$ .
Conjectureopencompound-poisson-processes nonparametric-inference statistical-inverse-problemsarXiv posted 2 days ago
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Optimal-rate conjecture for volatility estimation with polynomial kernels
Consider a microstructure-noise model whose kernel is … and whose volatility satisfies $\sigma\left(s,t\right)=\sigma\left(s\right)$ . Here $\alpha$ denotes the Hölder smoothness of…
Conjectureopenmicrostructure-noise statistical-inverse-problems volatility-estimationarXiv posted 2 days ago

4 problems

Adaptive minimax optimality conjecture for the SOLIT rule

Near-rate-optimality of the Smoluchowski displacement distribution estimator

Nickl–Reiß conjecture on a Donsker theorem for discretely observed compound Poisson processes

Optimal-rate conjecture for volatility estimation with polynomial kernels