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基于反射布朗运动的集合估计AI 解读

Summary We study the problem of estimating a compact set S⊂Rd from a trajectory of a reflected Brownian motion in S with reflections on the boundary of S. We establish consistency and rates of convergence for various estimators of S and its boundary. This problem has relevant applications in ecology in estimating the home range of an animal on the basis of tracking data. There are a variety of studies on the habitat of animals that employ the notion of home range. The paper…

庞加莱锥性质及其统计应用AI 解读

A domain $S\subset\mathbb{R}^{d}$ is said to fulfill the Poincaré cone property if any point in the boundary of $S$ is the vertex of a (finite) cone which does not otherwise intersects the closure $\bar{S}$. For more than a century, this condition has played a relevant role in the theory of partial differential equations, as a shape assumption aimed to ensure the existence of a solution for the classical Dirichlet problem on $S$. In a completely different setting, this paper…

长度与表面积估计的非参数方法AI 解读

The Minkowski content L0(G) of a body G⊂ℝd represents the boundary length (for d=2) or the surface area (for d=3) of G. A method for estimating L0(G) is proposed. It relies on a nonparametric estimator based on the information provided by a random sample (taken on a rectangle containing G) in which we are able to identify whether every point is inside or outside G. Some theoretical properties concerning strong consistency, L1-error and convergence rates are obtained. A…

位置参数的最优稳健 M 估计AI 解读

We find optimal robust estimates for the location parameter of n independent measurements from a common distribution F that belongs to a contamination neighborhood of a normal distribution. We follow an asymptotic minimax approach similar to Huber's but work with full neighborhoods of the central parametric model including nonsymmetric distributions. Our optimal estimates minimize monotone functions of the estimate's asymptotic variance and bias, which include asymptotic…

支撑集估计的插入式方法AI 解读

We suggest a new approach, based on the use of density estimators, for the problem of estimating the (compact) support of a multivariate density. This subject (motivated in terms of pattern analysis by Grenander) has interesting connections with detection and clustering. A natural class of density-based estimators is defined. Universal consistency results and convergence rates are established for these estimators, with respect to the usual measure-based metric $d_{\mu}$ betwe…

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…