We consider nonparametric estimation of the ridge of a probability density function for multivariate linear processes with long-range dependence. We derive functional limit theorems for estimated eigenvectors and eigenvalues of the Hessian matrix. We use these results to obtain the weak convergence for the estimated ridge and asymptotic simultaneous confidence regions.

中文翻译：

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多元长记忆过程的非参数脊估计

我们考虑对具有长程相关性的多元线性过程的概率密度函数脊的非参数估计。我们推导出 Hessian 矩阵的估计特征向量和特征值的功能极限定理。我们使用这些结果来获得估计脊和渐近同时置信区域的弱收敛。