Influence analysis in multivariate linear general models

In this paper two measures to highlight the possible effect of an observation on the UMVU estimate are proposed. Our study is based in expansions in terms of orthogonal polynomials for the UMVUE when sampling from a NEF-QVF. We obtain the conditional bias and the asymptotic mean sensitivity curve (AMSC) for the UMVUE. We observe that these measures depend on parametric function under consideration at the true and unknown value of the parameter. We study in detail their properties and relationships as well as to the Hampel's influence function. In fact, we note that the AMSC also verifies for the UMVUE in the NEF-QVF some of most relevant properties of influence function. Also a case-deletion influence diagnostic and some simulations are included to illustrate our results.

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“…Fixed μ ∈ Ω and k = k(μ) = min{j ∈ Z + : h (j ) (μ) = 0}, let us look again at (14) and note that this can be written as…”

Section: Comments On the Previous Results Given In This Sectionmentioning

confidence: 99%

“…As examples we can cite the papers by Muñoz-Pichardo et al [14] in multivariate linear general models, Jiménez-Gamero et al [15] in regression with complex designs, and Moreno-Rebollo et al [16] in survey sampling. The IF is a powerful tool in robustness, however it has the disadvantage of being built upon statistical functionals.…”

Section: Introductionmentioning

confidence: 97%

Some measures of robustness for unbiased estimators in one-parameter natural exponential families with quadratic variance function

Barranco-Chamorro

Rebollo

2008

Journal of Mathematical Analysis and Applications

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“…See Caroni (1987), Hossain and Naik (1989), Barret and Ling (1992), Muñoz-Pichardo et al (2000), Jiménez-Gamero et al (2002), and references therein. By far the most popular approach is that of measuring the change in some feature of the analysis upon deletion of one or more of the observations.…”

Section: Introductionmentioning

confidence: 97%

Influence Measures Based on Cressie-Read Divergence Measures in Multivariate Linear Model

García-Heras

García

Muñoz

et al. 2006

Communications in Statistics - Theory and Methods

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We define a new family of influence measures based on the divergence measures, in the multivariate general linear model. Influence measures are obtained by quantifying the divergence between the sample distribution of an estimate obtained with all the observations and the sample distribution of the same estimate obtained without any observation. This approach is applied to best linear unbiased estimates of estimable functions. Therefore, these diagnostics can be applied to every statistical multivariate technique that can be formulated like this kind of model. Some examples are considered to clarify the applicability of the introduced diagnostics.

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Influence diagnostics in regression with complex designs through conditional bias

Reyes

Muñoz

Rebollo

2005

TEST

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Influence analysis in multivariate linear general models

Cited by 7 publications

References 5 publications

Some measures of robustness for unbiased estimators in one-parameter natural exponential families with quadratic variance function

Some measures of robustness for unbiased estimators in one-parameter natural exponential families with quadratic variance function

Influence Measures Based on Cressie-Read Divergence Measures in Multivariate Linear Model

Influence diagnostics in regression with complex designs through conditional bias

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