α-混合过程条件密度的估计及其性质

On α-Mixing Process's Conditional Density Estimator and Its Properties

本文在{X_t,t∈N}是一个严平稳过程的假设下,用核估计的方法对未来状态X_(N+T)的条件密度进行估计.在假设{X_t,t∈N}是α-混合过程的情况下,讨论了过程有限维密度核估计的期望与方差,以及过程条件密度核估计的偏及均方误差.在一定条件下,证明了估计的弱收敛性.

This paper applies the kernel method to estimate the conditional density of future state XN＋T, under strictly stationary assumption. In the case of assuming （Xt,t ∈ N} to be an α-mixing process, we discuss the expectation and variance of the kernel estimator of the process＇s finite dimensional density, and the bias, MSE of the kernel estimator of the process＇s conditional density. We also prove the weak convergency of the estimator under some given conditions.