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Register a new userMinimax density estimation for growing dimension
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Added by
Daniel McDonald
Publication date
2017
fields
Mathematical Statistics
and research's language is
English
Authors
Daniel J. McDonald
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This paper presents minimax rates for density estimation when the data dimension $d$ is allowed to grow with the number of observations $n$ rather than remaining fixed as in previous analyses. We prove a non-asymptotic lower bound which gives the worst-case rate over standard classes of smooth densities, and we show that kernel density estimators achieve this rate. We also give oracle choices for the bandwidth and derive the fastest rate $d$ can grow with $n$ to maintain estimation consistency.
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