Density Estimation in the $L^\infty$ Norm for Dependent Data with Applications to the Gibbs Sampler
Density Estimation in the $L^\infty$ Norm for Dependent Data with Applications to the Gibbs Sampler
This paper investigates the density estimation problem in the $L^\infty$ norm for dependent data. It is shown that the iid optimal minimax rates are also optimal for smooth classes of stationary sequences satisfying certain $\beta$-mixing (or absolutely regular) conditions. Moreover, for given $\beta$-mixing coefficients, bounds on uniform convergence rates of …