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  1. Zdravkovic L, Kontoe S (Ed.)
    Free, publicly-accessible full text available June 22, 2024
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  6. We study the bias of the isotonic regression estimator. While there is extensive work characterizing the mean squared error of the iso- tonic regression estimator, relatively little is known about the bias. In this paper, we provide a sharp characterization, proving that the bias scales as O(n−β/3) up to log factors, where 1 ≤ β ≤ 2 is the exponent correspond- ing to H ̈older smoothness of the underlying mean. Importantly, this result only requires a strictly monotone mean and that the noise distribution has subexponential tails, without relying on symmetric noise or other restrictive assumptions. 
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  7. Abstract

    We present the results of a search for core-collapse supernova neutrinos, using long-term KamLAND data from 2002 March 9 to 2020 April 25. We focus on the electron antineutrinos emitted from supernovae in the energy range of 1.8–111 MeV. Supernovae will make a neutrino event cluster with the duration of ∼10 s in the KamLAND data. We find no neutrino clusters and give the upper limit on the supernova rate to be 0.15 yr−1with a 90% confidence level. The detectable range, which corresponds to a >95% detection probability, is 40–59 kpc and 65–81 kpc for core-collapse supernovae and failed core-collapse supernovae, respectively. This paper proposes to convert the supernova rate obtained by the neutrino observation to the Galactic star formation rate. Assuming a modified Salpeter-type initial mass function, the upper limit on the Galactic star formation rate is <(17.5–22.7)Myr−1with a 90% confidence level.

     
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