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函数型主成分分析的 S 估计量AI 解读

Principal component analysis is a widely used technique that provides an optimal lower-dimensional approximation to multivariate or functional datasets. These approximations can be very useful in identifying potential outliers among high-dimensional or functional observations. In this article, we propose a new class of estimators for principal components based on robust scale estimators. For a fixed dimension q, we robustly estimate the q-dimensional linear space that…

稳健函数型主成分：投影寻踪方法AI 解读

In many situations, data are recorded over a period of time and may be regarded as realizations of a stochastic process. In this paper, robust estimators for the principal components are considered by adapting the projection pursuit approach to the functional data setting. Our approach combines robust projection-pursuit with different smoothing methods. Consistency of the estimators are shown under mild assumptions. The performance of the classical and robust procedures are…

广义部分线性模型中的稳健估计AI 解读

In this paper, we introduce a family of robust estimates for the parametric and nonparametric components under a generalized partially linear model, where the data are modeled by yi|(xi, ti)∼F(⋅, μi) with μi=H(η(ti)+xiTβ), for some known distribution function F and link function H. It is shown that the estimates of β are root-n consistent and asymptotically normal. Through a Monte Carlo study, the performance of these estimators is compared with that of the classical ones.

混合过程下非参数模型稳健估计量的渐近分布AI 解读

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AI 解读

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…

非标准条件下非正则广义极大似然估计的渐近行为AI 解读

In this paper we generalize Huber's (1967) results to include the nonregular case. Resistant estimators which turn out to be asymptotically unbiased in a neighbourhood of the model are given for some univariate models. Their order of consistency achieves the rate of the maximum likelihood estimates. Moreover, some of the estimates are asymptotically efficient under the central model, in the sense that they have the same asymptotic distribution as the maximum likelihood…

非标准条件下非正则广义最大似然估计的渐近行为AI 解读

In this paper we generalize Huber's (1967) results to include the nonregular case. Resistant estimators which turn out to be asymptotically unbiased in a neighbourhood of the model are given for some univariate models. Their order of consistency achieves the rate of the maximum likelihood estimates. Moreover, some of the estimates are asymptotically efficient under the central model, in the sense that they have the same asymptotic distribution as the maximum likelihood…

随机过程的定性稳健性AI 解读

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…