排序方式: 共有36条查询结果,搜索用时 390 毫秒
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André Lucas 《统计学通讯:理论与方法》2013,42(10):2363-2380
This paper considers the robustness properties in the time series context of the least median of squares (LMS) estimator. The influence function of the LMS estimator is derived under additive outlier contamination. This influence function is redescending and bounded for fixed values of the AR parameters. The gross-error sensitivity, however, is an unbounded function of the AR parameters. In order to asses the global robustness behavior of the LMS estimator, we consider several notions of breakdown. The breakdown points of the LMS estimator depend on the value of the underlying AR parameter. Generally, the breakdown point is below one half for high values of the AR parameter. The bias curves of the LMS estimator reveal, however, that the magnitude of outliers has to be considerable in order to cause breakdown. 相似文献
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Ordinal regression is used for modelling an ordinal response variable as a function of some explanatory variables. The classical technique for estimating the unknown parameters of this model is Maximum Likelihood (ML). The lack of robustness of this estimator is formally shown by deriving its breakdown point and its influence function. To robustify the procedure, a weighting step is added to the Maximum Likelihood estimator, yielding an estimator with bounded influence function. We also show that the loss in efficiency due to the weighting step remains limited. A diagnostic plot based on the Weighted Maximum Likelihood estimator allows to detect outliers of different types in a single plot. 相似文献
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Clint W. Coakley Thomas P. Hettmansperger 《Australian & New Zealand Journal of Statistics》1994,36(2):225-233
The breakdown point of an estimator is the smallest fraction of contamination that can force the value of the estimator beyond the boundary of the parameter space. It is well known that the highest possible breakdown point, under equivariance restrictions, is 50% of the sample. However, this upper bound is not always attainable. We give an example of an estimation problem in which the highest possible attainable breakdown point is much less than 50% of the sample. For hypothesis testing, we discuss the resistance of a test and propose new definitions of resistance. The maximum resistance to rejection (acceptance) is the smallest fraction of contamination necessary to force a test to reject (fail to reject) regardless of the original sample. We derive the maximum resistances of the t-test and sign test in the one-sample problem and of the t-test and Mood test in the two-sample problem. We briefly discuss another measure known as the expected resistance. 相似文献
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R.A. Bailey Katharina Schiffl Ralf-Dieter Hilgers 《Journal of statistical planning and inference》2013
Two-colour microarray experiments form an important tool in gene expression analysis. Due to the high risk of missing observations in microarray experiments, it is fundamental to concentrate not only on optimal designs but also on designs which are robust against missing observations. As an extension of Latif et al. (2009), we define the optimal breakdown number for a collection of designs to describe the robustness, and we calculate the breakdown number for various D-optimal block designs. We show that, for certain values of the numbers of treatments and arrays, the designs which are D-optimal have the highest breakdown number. Our calculations use methods from graph theory. 相似文献
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Weiyan Mu 《统计学通讯:理论与方法》2013,42(5):1033-1043
Penalized least squares estimators are sensitive to the influence of outliers like the ordinary least squares estimator. We propose a sparse regression estimator for robust variable selection and estimation based on a robust initial estimator. It is proven that our estimator has at least the same breakdown value as the initial estimator. Numerical examples are presented to illustrate our method. 相似文献
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In univariate statistics, the trimmed mean has long been regarded as a robust and efficient alternative to the sample mean. A multivariate analogue calls for a notion of trimmed region around the center of the sample. Using Tukey's depth to achieve this goal, this paper investigates two types of multivariate trimmed means obtained by averaging over the trimmed region in two different ways. For both trimmed means, conditions ensuring asymptotic normality are obtained; in this respect, one of the main features of the paper is the systematic use of Hadamard derivatives and empirical processes methods to derive the central limit theorems. Asymptotic efficiency relative to the sample mean as well as breakdown point are also studied. The results provide convincing evidence that these location estimators have nice asymptotic behavior and possess highly desirable finite-sample robustness properties; furthermore, relative to the sample mean, both of them can in some situations be highly efficient for dimensions between 2 and 10. 相似文献
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《Journal of Statistical Computation and Simulation》2012,82(5):311-332
This paper examines robust techniques for estimation and tests of hypotheses using the family of generalized Kullback-Leibler (GKL) divergences. The GKL family is a new group of density based divergences which forms a subclass of disparities defined by Lindsay (1994). We show that the corresponding minimum divergence estimators have a breakdown point of 50% under the model. The performance of the proposed estimators and tests are investigated through an extensive numerical study involving real-data examples and simulation results. The results show that the proposed methods are attractive choices for highly efficient and robust methods. 相似文献