Nonparametric Density Estimation for a Long-Range Dependent Linear Process
Nonparametric Density Estimation for a Long-Range Dependent Linear Process
复制标题
长程相关线性过程的非参数密度估计
DOI：
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
Toshio Honda
中科院分区：
文献类型：
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作者：
Toshio Honda
利用核估计对长程相依线性过程的边际密度函数进行了估计。我们假设创新是独立同分布的。然后，它是已知的，在核密度估计的MISE的样本均值项是占主导地位的依赖性是超过一定的水平，这取决于带宽和MISE具有渐近相同的形式为i.i.d.当依赖性低于水平时的观察结果。我们称后者为依赖性不是很强的情况，并在本文中重点关注它。我们证明了核密度估计的渐近分布与i.i.d.相同。观察和长期依赖的效果没有出现。此外，我们还描述了弱相依线性过程的一些结果。
We estimate the marginal density function of a long-range dependent linear process by the kernel estimator. We assume the innovations are i.i.d. Then it is known that the term of the sample mean is dominant in the MISE of the kernel density estimator when the dependence is beyond some level which depends on the bandwidth and that the MISE has asymptotically the same form as for i.i.d. observations when the dependence is below the level. We call the latter the case where the dependence is not very strong and focus on it in this paper. We show that the asymptotic distribution of the kernel density estimator is the same as for i.i.d. observations and the effect of long-range dependence does not appear. In addition we describe some results for weakly dependent linear processes.