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Breakdown and Groups
, 2002
"... The concept of breakdown point was... In this paper we argue that this success is intimately connected to the fact that the translation and affine groups act on the sample space and give rise to a definition of equivariance for statistical functionals. For such functionals a nontrivial upper bound f ..."
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Cited by 9 (2 self)
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The concept of breakdown point was... In this paper we argue that this success is intimately connected to the fact that the translation and affine groups act on the sample space and give rise to a definition of equivariance for statistical functionals. For such functionals a nontrivial upper bound for the breakdown point can be shown. In the absence of such a group structure a breakdown point of one is attainable and this is perhaps the decisive reason why the concept of breakdown point in other situations has not proved as successful. Even if a natural group is present it is often not sufficiently large to allow a nontrivial upper bound for the breakdown point. One exception to this is the problem of the autocorrelation structure of time series where we derive a nontrivial upper breakdown point using the group of realizable linear filters. The paper is formulated in an abstract manner to emphasize the role of the group and the resulting equivariance structure
Predictive SpatioTemporal Models for Spatially Sparse Environmental Data
, 2005
"... We present a family of spatiotemporal models which are geared to provide timeforward predictions in environmental applications where data is spatially sparse but temporally rich. That is ..."
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Cited by 8 (5 self)
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We present a family of spatiotemporal models which are geared to provide timeforward predictions in environmental applications where data is spatially sparse but temporally rich. That is
Robustness properties of dispersion estimators
, 1999
"... In this paper, we derive the in uence function of dispersion estimators, based on a scale approach. The relation between the grosserror sensitivity of dispersion estimators and the one of the underlying scale estimator is described. We show that for the bivariate Gaussian distributions, the asympto ..."
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Cited by 2 (2 self)
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In this paper, we derive the in uence function of dispersion estimators, based on a scale approach. The relation between the grosserror sensitivity of dispersion estimators and the one of the underlying scale estimator is described. We show that for the bivariate Gaussian distributions, the asymptotic variance of covariance estimators is minimal in the independent case, and is strictly increasing with the absolute value of the underlying covariance. The behavior of the asymptotic variance of correlation estimators seems to be the opposite, i.e. maximal for independent data, and strictly decreasing with the absolute value of the underlying correlation. In particular, dispersion estimators based on Mestimators of scale are studied closely. The one based on the median absolute deviation is the most Brobust in the class of symmetric estimators. Some other examples are analyzed, based on the maximum likelihood and the Welsch estimator of scale.
Indirect Inference for SpatioTemporal Autoregression Models
"... Introduction In this note we introduce a new inferential method for STAR (spatiotemporal autoregression) models. Due to the complexity of such models the maximum likelihood estimation is difficult to undertake when several nearest neighbours are included in the model, see Ali (1979). Moreover, onl ..."
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Introduction In this note we introduce a new inferential method for STAR (spatiotemporal autoregression) models. Due to the complexity of such models the maximum likelihood estimation is difficult to undertake when several nearest neighbours are included in the model, see Ali (1979). Moreover, only approximate likelihoods are available in practice because of the observations lying on the edges of the spatial domain. On the other hand, simpler estimation methods such as least squares and YuleWalker are not generally consistent. With this background, we propose the use of an inferential method based on an auxiliary model whose parameters can be consistently estimated with YuleWalker. From this estimation, consistent estimators for the parameters of the STAR model of interest are then retrieved with the help of simulated data. The method and its asymptotic theory are presented in Section 2. In Section 3 we illustrate its small sample properties with a limited Monte Carlo experime
Comprehensive Definitions of BreakdownPoints for Independent and Dependent Observations
, 2000
"... We provide a new definition of breakdown in finite samples with an extension to asymptotic breakdown. Previous definitions center around defining a critical region for either the parameter or the objective function. If for a particular outlier constellation the critical region is entered, breakdown ..."
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We provide a new definition of breakdown in finite samples with an extension to asymptotic breakdown. Previous definitions center around defining a critical region for either the parameter or the objective function. If for a particular outlier constellation the critical region is entered, breakdown is said to occur. In contrast to the traditional approach, we leave the definition of the critical region implicit. Our definition encompasses all previous definitions of breakdown in both linear and nonlinear regression settings. In some cases, it leads to a different notion of breakdown than other procedures available. An advantage is that our new definition also applies to models for dependent observations (timeseries, spatial statistics) where current breakdown definitions typically fail. We illustrate our points using examples from linear and nonlinear regression as well as timeseries and spatial statistics.
Visualizing Influential Observations in Dependent Data
, 2009
"... We introduce the hairplot to visualize influential observations in dependent data. It consists of all trajectories of the value of an estimator when each observation is modified in turn by an additive perturbation. We define two measures of influence: the local influence which describes the rate of ..."
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We introduce the hairplot to visualize influential observations in dependent data. It consists of all trajectories of the value of an estimator when each observation is modified in turn by an additive perturbation. We define two measures of influence: the local influence which describes the rate of departure from the original estimate due to a small perturbation of each observation; and the asymptotic influence which indicates the influence on the original estimate of the most extreme contamination for each observation. The cases of estimators defined as quadratic forms or ratios of quadratic forms are investigated in detail. Sample autocovariances, covariograms and variograms belong to the first case. Sample autocorrelations, correlograms, and indices of spatial autocorrelation such as Moran’s I belong to the second case. We illustrate our approach on various datasets from time series analysis and spatial statistics.