We consider inference for local maxima of the marginal density function of strongly dependent linear processes. Weak consistency of the estimated modular set and the number of modes is derived. A uniform reduction principle for kernel density estimators is used to obtain confidence sets for the set of modes. The results can be extended to multivariate modes. Simulations illustrate the asymptotic results.

中文翻译：

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长记忆模式下的推理

我们考虑对强相关线性过程的边际密度函数的局部最大值的推断。推导出估计的模集和模式数的弱一致性。核密度估计器的统一归约原则用于获得模式集的置信集。结果可以扩展到多变量模式。模拟说明了渐近结果。