4 problems

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Conjecture on the sharp upper bound for the Kozachenko–Leonenko estimator
Let $n$ be the sample size, let $s\in(0,2]$ be the smoothness parameter, and let $d$ be the dimension. Consider the fixed- $k$ Kozachenko–Leonenko nearest-neighbor estimator of diff…
Conjectureopeninformation-theory nearest-neighbor-methods nonparametric-estimationarXiv posted 2 days ago
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Bayes-consistency conjecture for GKN
Let textup{{textsf{GKN}}} be the earlier gamma-net-based classification algorithm described in the paper, which removes a minimum vertex cover so that the remaining sample is gamma…
Conjectureopennearest-neighbor-methods sample-compression statistical-learning-theoryarXiv posted 2 days ago
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Boundary-away chi-square conjecture for nearest-neighbour statistics
Let $X_1,\ldots,X_n$ be an $i.i.d.$ sample from a distribution on a manifold $M$ with nonempty boundary, and let $\delta_{i,k_n}$ denote the statistic defined in the paper for the…
Conjectureopenasymptotic-statistics boundary-detection nearest-neighbor-methodsarXiv posted 2 days ago
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The k-nearest-neighbor rate conjecture for smooth regression functions
k-nearest-neighbor rate conjecture. There exists a choice of the $k$ -NN estimator such that
Conjectureopennearest-neighbor-methods nonparametric-statistics regression-estimationarXiv posted 2 days ago

Conjecture on the sharp upper bound for the Kozachenko–Leonenko estimator