Robust estimators and tests for bivariate copulas based on likelihood depth

Denecke, Liesa; Müller, Christine H.

doi:10.1016/j.csda.2011.04.005

Cited by 13 publications

(6 citation statements)

References 19 publications

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“…Although d S (θ, z * ) is a U-statistic, it is only in few cases not a degenerated U-statistic, see Denecke and Müller (2011, 2013, 2014. In most cases, d S (θ, z * ) is a degenerated U-statistic and its asymptotic distribution must be determined by a spectral decomposition of the conditional expectation.…”

Section: Introductionmentioning

confidence: 99%

“…Starting with the halfspace depth of Tukey (1975) for multivariate data, meanwhile many depth notions were proposed. There exist depth notions for regression as in Rousseeuw and Hubert (1999), for generalized linear models as in Müller (2005), for estimation equations as in Lin and Chen (2006), for functional data as in López-Pintado and Romo (2009) or Claeskens et al (2014), for copulas as in Denecke and Müller (2011), and for correlation as in Denecke and Müller (2014). Further depth can be used to estimate quantiles, also in regression, as discussed by Hallin et al (2010).…”

Section: Introductionmentioning

confidence: 99%

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Simplified simplicial depth for regression and autoregressive growth processes

Kustosz

Müller

Wendler

2016

Journal of Statistical Planning and Inference

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We simplify simplicial depth for regression and autoregressive growth processes in two directions. At first we show that often simplicial depth reduces to counting the subsets with alternating signs of the residuals. The second simplification is given by not regarding all subsets of residuals. By consideration of only special subsets of residuals, the asymptotic distributions of the simplified simplicial depth notions are normal distributions so that tests and confidence intervals can be derived easily. We propose two simplifications for the general case and a third simplification for the special case where two parameters are unknown. Additionally, we derive conditions for the consistency of the tests. We show that the simplified depth notions can be used for polynomial regression, for several nonlinear regression models, and for several autoregressive growth processes. We compare the efficiency and robustness of the different simplified versions by a simulation study concerning the Michaelis-Menten model and a nonlinear autoregressive process of order one.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Simplified simplicial depth for regression and autoregressive growth processes

Kustosz

Müller

Wendler

2016

Journal of Statistical Planning and Inference

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“…In the semiparametric copulabased multivariate dynamic (SCOMDY) framework ( [9]), [22] built a minimum density power divergence estimator which shows some resistance to some types of outliers. [14] proposed a parametric robust estimation method based on likelihood depth ( [29]). Recently, [18] have considered robust and nonparametric estimation of the coefficient of tail dependence in presence of random covariates, that may be a way of estimating copulas for some particular models.…”

Section: Contextmentioning

confidence: 99%

“…that is integrable because K U and its partial derivatives are integrable. As before, use again the identity (14) and the dominated convergence theorem to show that θ → (w, θ) is continuous on Θ.…”

Section: B Proof Of Propositionmentioning

confidence: 99%

Estimation of copulas via Maximum Mean Discrepancy

Alquier,

Chérief-Abdellatif,

Derumigny

et al. 2020

Preprint

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This paper deals with robust inference for parametric copula models. Estimation using Canonical Maximum Likelihood might be unstable, especially in the presence of outliers. We propose to use a procedure based on the Maximum Mean Discrepancy (MMD) principle. We derive non-asymptotic oracle inequalities, consistency and asymptotic normality of this new estimator. In particular, the oracle inequality holds without any assumption on the copula family, and can be applied in the presence of outliers or under misspecification. Moreover, in our MMD framework, the statistical inference of copula models for which there exists no density with respect to the Lebesgue measure on [0, 1] d , as the Marshall-Olkin copula, becomes feasible. A simulation study shows the robustness of our new procedures, especially compared to pseudo-maximum likelihood estimation. An R package implementing the MMD estimator for copula models is available.

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“…However, the simplicial depth often is a degenerated U‐statistic. There are only few cases where this is not the case (Denecke and Müller, ; ; ; ). For regression problems, the simplicial depth is a degenerated U‐statistic.…”

Section: Introductionmentioning

confidence: 99%

Tests Based on Simplicial Depth for AR(1) Models With Explosion

Kustosz

Leucht

Müller

2016

Journal Time Series Analysis

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We propose an outlier robust and distributions-free test for the explosive AR(1) model with intercept based on simplicial depth. In this model, simplicial depth reduces to counting the cases where three residuals have alternating signs. Using this, it is shown that the asymptotic distribution of the test statistic is given by an integrated two-dimensional Gaussian process. Conditions for the consistency of the test are given and the power of the test at finite samples is compared with five alternative tests, using errors with normal distribution, contaminated normal distribution, and Fréchet distribution in a simulation study. The comparisons show that the new test outperforms all other tests in the case of skewed errors and outliers. Although here we deal with the AR(1) model with intercept only, the asymptotic results hold for any simplicial depth which reduces to alternating signs of three residuals.

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Robust estimators and tests for bivariate copulas based on likelihood depth

Cited by 13 publications

References 19 publications

Simplified simplicial depth for regression and autoregressive growth processes

Simplified simplicial depth for regression and autoregressive growth processes

Estimation of copulas via Maximum Mean Discrepancy

Tests Based on Simplicial Depth for AR(1) Models With Explosion

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