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混合过程下非参数模型稳健估计量的渐近分布
In this paper we obtain the asymptotic distribution of robust nonparametric autoregression estimators for dependent observations. Weights based on kernel and nearest-neighbor methods are considered.
依赖观测下的稳健非参数回归估计
Robust nonparametric estimators for regression and autoregression are proposed for $\varphi$- and $\alpha$-mixing processes. Two families of $M$-type robust equivariant estimators are considered: (i) estimators based on kernel methods and (ii) estimators based on $k$-nearest neighbor kernel methods. Strong consistency of both families is proved under mild conditions. For the first class the result is true under no assumptions whatsoever on the distribution of the…
随机过程的定性稳健性
In this paper we generalize Hampel's concept of qualitative robustness of a sequence of estimators to the case of stochastic processes with non-i.i.d. observations, defining appropriate metrics between samples. We also present a different approach to qualitative robustness which formalizes the notion of resistance. We give two definitions based on this approach: strong and weak resistance. We show that for estimating a finite dimensional real parameter, $\pi$-robustness is…