  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.
