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
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DOI：
10.1214/aos/1176349146
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发表时间：
1993-06
影响因子：
4.5
通讯作者：
Bin Yu
中科院分区：
文献类型：
--
作者：
Bin Yu
本文研究了相依数据在LX范数下的密度估计问题。证明了对于满足某些，8-混合（或绝对正则）条件的平稳序列光滑类，iid最优minimax速率也是最优的.此外，对于给定的3-混合系数，核估计的一致收敛速度的界计算的混合系数。所得到的速率和界不仅用于估计密度，而且用于估计其导数。结果，然后应用到与吉布斯采样器的问题，给出统一的收敛速度。
This paper investigates the density estimation problem in the LX norm for dependent data. It is shown that the iid optimal minimax rates are also optimal for smooth classes of stationary sequences satisfying certain ,8-mixing (or absolutely regular) conditions. Moreover, for given 3-mixing coefficients, bounds on uniform convergence rates of kernel estimators are computed in terms of the mixing coefficients. The rates and the bounds obtained are not only for estimating the density but also for its derivatives. The results are then applied to give uniform convergence rates in problems associated with the Gibbs sampler.