Fast and robust estimation of the multivariate errors in variables model

Croux, Christophe; Fekri, M.; Ruiz‐Gazen, Anne

doi:10.1007/s11749-009-0155-9

Cited by 14 publications

(8 citation statements)

References 24 publications

(25 reference statements)

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“…Finally, another perspective is to consider multivariate errors-in-variables models, which allow incorporating measurement errors in the response and the explanatory variables. A possible approach is proposed in Croux et al (2010).…”

Section: Discussionmentioning

confidence: 99%

Multivariate Student versus Multivariate Gaussian Regression Models with Application to Finance

Nguyen

Ruiz‐Gazen

Thomas‐Agnan

et al. 2019

JRFM

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To model multivariate, possibly heavy-tailed data, we compare the multivariate normal model (N) with two versions of the multivariate Student model: the independent multivariate Student (IT) and the uncorrelated multivariate Student (UT). After recalling some facts about these distributions and models, known but scattered in the literature, we prove that the maximum likelihood estimator of the covariance matrix in the UT model is asymptotically biased and propose an unbiased version. We provide implementation details for an iterative reweighted algorithm to compute the maximum likelihood estimators of the parameters of the IT model. We present a simulation study to compare the bias and root mean squared error of the ensuing estimators of the regression coefficients and covariance matrix under several scenarios of the potential data-generating process, misspecified or not. We propose a graphical tool and a test based on the Mahalanobis distance to guide the choice between the competing models. We also present an application to model vectors of financial assets returns.

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Section: Discussionmentioning

confidence: 99%

Multivariate Student versus Multivariate Gaussian Regression Models with Application to Finance

Nguyen

Ruiz‐Gazen

Thomas‐Agnan

et al. 2019

JRFM

Self Cite

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“…However, S-estimators are computed using inefficient algorithms and M-estimators have low breakdown point. Another possibility can be found in [20], where the projection-pursuit approach is used, which is also suitable for more than one response variable. In order to keep the structure of the paper consistent, but also to benefit from the better statistical properties of the MM-estimates, which will be combined with fast and robust bootstrap, we decided to follow the above (classical) approach in order to develop robust orthogonal regression in orthonormal coordinates.…”

Section: Orthogonal Regressionmentioning

confidence: 99%

“…[22] Among other possibilities like, [20,23,24] in the following the MM-estimators [25] are employed for this purpose. The reason for choosing MM-estimators is that they are highly efficient when the errors have a normal distribution, their breakdown point is 0.5 and they have bounded influence function.…”

Section: Orthogonal Regressionmentioning

confidence: 99%

Classical and robust orthogonal regression between parts of compositional data

et al. 2016

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The different parts (variables) of a compositional data set cannot be considered independent from each other, since only the ratios between the parts constitute the relevant information to be analysed. Practically, this information can be included in a system of orthonormal coordinates. For the task of regression of one part on other parts, a specific choice of orthonormal coordinates is proposed which allows for an interpretation of the regression parameters in terms of the original parts. In this context, orthogonal regression is appropriate since all compositional parts -also the explanatory variables -are measured with errors. Besides classical (least-squares based) parameter estimation, also robust estimation based on robust principal component analysis is employed. Statistical inference for the regression parameters is obtained by bootstrap; in the robust version the fast and robust bootstrap procedure is used. The methodology is illustrated with a data set from macroeconomics. ARTICLE HISTORY

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“…Fekri and Ruiz-Gazen (2004) got the robust estimators of parameters from robust estimators of multivariate location and scatter. Croux et al (2010) proposed a projection-pursuit based estimation procedure of the multivariate EV model. Cui (1997a) also studied the robustness of the M-estimator and obtained the asymptotic properties via the orthogonal regression.…”

Section: Introductionmentioning

confidence: 99%

t-Type corrected-loss estimation for error-in-variable model

Jin

Zhu

Tong

et al. 2016

Communications in Statistics - Theory and Methods

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In this paper, we consider a linear model in which the covariates are measured with errors. We propose a t-type corrected-loss estimation of the covariate effect, when the measurement error follows the Laplace distribution. The proposed estimator is asymptotically normal. In practical studies, some outliers that diminish the robustness of the estimation occur. Simulation studies show that the estimators are resistent to vertical outliers and an application of Six-Minute Walk test is presented to show that the proposed method performs well.

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Fast and robust estimation of the multivariate errors in variables model

Abstract: Errors in variables, Multivariate statistics, Principal components, Projection-pursuit, Robustness, 62G35, 62H99,

Cited by 14 publications

References 24 publications

Multivariate Student versus Multivariate Gaussian Regression Models with Application to Finance

Multivariate Student versus Multivariate Gaussian Regression Models with Application to Finance

Classical and robust orthogonal regression between parts of compositional data

t-Type corrected-loss estimation for error-in-variable model

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