New robust tests for the parameters of the Weibull distribution for complete and censored data

Denecke, Liesa; Müller, Christine H.

doi:10.1007/s00184-013-0454-8

Cited by 6 publications

(2 citation statements)

References 31 publications

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“…A recent exception is the work of Ghosh et al (2017), where a robust version of the Wald test based on the minimum density power divergence approach of Basu et al (2006) was studied. To the best of our knowledge, other contributions to the literature were mainly designed for a specific model; see, for example, Denecke and Müller (2014) for the Weibull case.…”

Section: Testingmentioning

confidence: 99%

Robust inference with censored survival data

Deléamont

Ronchetti

2022

Scandinavian J Statistics

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Randomly censored survival data appear in a wide variety of applications in which the time until the occurrence of a certain event is not completely observable.In this paper, we assume that the statistician observes a possibly censored survival time along with a censoring indicator. In this setting, we study a class of M-estimators with a bounded influence function, in the spirit of the infinitesimal approach to robustness. We outline the main asymptotic properties of the robust M-estimators and characterize the optimal B-robust estimator according to two possible measures of sensitivity. Building on these results, we define robust testing procedures which are natural counterparts to the classical Wald, score, and likelihood ratio tests. The empirical performance of our robust estimators and tests is assessed in two extensive simulation studies. An application to data from a well-known medical study on head and neck cancer is also presented.

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Section: Testingmentioning

confidence: 99%

Robust inference with censored survival data

Deléamont

Ronchetti

2022

Scandinavian J Statistics

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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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The risk function of the goodness-of-fit tests for tail models

Hoffmann

Börner

2020

Stat Papers

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This paper contributes to answering a question that is of crucial importance in risk management and extreme value theory: How to select the threshold above which one assumes that the tail of a distribution follows a generalized Pareto distribution. This question has gained increasing attention, particularly in finance institutions, as the recent regulative norms require the assessment of risk at high quantiles. Recent methods answer this question by multiple uses of the standard goodness-of-fit tests. These tests are based on a particular choice of symmetric weighting of the mean square error between the empirical and the fitted tail distributions. Assuming an asymmetric weighting, which rates high quantiles more than small ones, we propose new goodness-of-fit tests and automated threshold selection procedures. We consider a parameterized family of asymmetric weight functions and calculate the corresponding mean square error as a loss function. We then explicitly determine the risk function as the finite sample expected value of the loss function. Finally, the risk function can be used to discuss the question of which symmetric or asymmetric weight function and, thus, which goodness-of-fit test should be used in a new method for determining the threshold value.

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New robust tests for the parameters of the Weibull distribution for complete and censored data

Cited by 6 publications

References 31 publications

Robust inference with censored survival data

Robust inference with censored survival data

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

The risk function of the goodness-of-fit tests for tail models

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