Strong consistency of the general rank estimator

Bindele, Huybrechts F.

doi:10.1080/03610926.2014.999091

Cited by 8 publications

(5 citation statements)

References 21 publications

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“…The proof of this theorem follows the lines of Bindele () along with Lemma given in Appendix whose proof can also be found in Andrews () and Newey & McFadden (). The proofs are therefore omitted.…”

Section: Asymptotic Propertiesmentioning

confidence: 95%

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Rank‐based inference with responses missing not at random

Bindele

Adekpedjou

2018

Can J Statistics

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Missing data have become almost inevitable whenever data are collected. In this paper, interest is given to responses missing not at random in the context of regression modeling. Many of the existing methods for estimating the model parameters lack robustness or efficiency. We propose a robust and efficient approach towards estimating the true regression parameters when some responses in the regression model are missing not at random. Large sample properties of the proposed estimator are established under mild regularity conditions. Monte Carlo simulation experiments are carried out and they showed that the proposed estimator is more efficient than the least squares estimator whenever the model error distribution is heavy tailed, contaminated or when data contain gross outliers. Finally, the method is illustrated using the ACTG protocol 315 data. The Canadian Journal of Statistics 46: 501–528; 2018 © 2018 Statistical Society of Canada

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Section: Asymptotic Propertiesmentioning

confidence: 95%

“…The asymptotic properties of

{\overset{β}{true}}_{n}

have been extensively studied in the literature, specifically for linear models (Hettmansperger & McKean ). For general regression models, the asymptotic properties of

{\overset{β}{true}}_{n}

are established by Bindele & Abebe () and Bindele ().…”

Section: Imputation Under Mnarmentioning

confidence: 99%

Rank‐based inference with responses missing not at random

Bindele

Adekpedjou

2018

Can J Statistics

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“…An R suite of function is developed for WW estimation and testing of hypotheses, diagnostic measures, and residual analysis is available. Bindele [23] considered rank estimator of the general linear regression model. e author established strong consistency of the rank estimator is under mild conditions.…”

Section: Introductionmentioning

confidence: 99%

Development of New Robust Optimal Score Function for the Weibull Distributed Error Term in Multilevel Models

Saleem

Sherwani

Amin

et al. 2021

Mathematical Problems in Engineering

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A popular robust estimation technique for linear models is the rank-based method as an alternative to the ordinary least square (OLS) and restricted maximum likelihood (REML) in the presence of extreme observations. This method is applied in machine reliability analysis and quantum engineering, especially in artificial intelligence and optimization problems where outliers are commonly observed. This technique is also extended for the multilevel model, where the shape of error distribution contributes a significant role in more efficient estimation. In this study, we proposed the Weibull score function for the Weibull distributed error terms in the multilevel model. The efficiency of the proposed score function is compared with the existing Wilcoxon score function and the traditional method REML via Monte Carlo simulations after adding simulated extreme observations. For small values of shape parameter in Weibull distribution of error term showing the presence of outliers, the Weibull score function was found to be efficient as compared to the Wilcoxon and REML methods. However, for a large value of shape parameter, Wilcoxon score appeared either equally efficient than the Weibull score function. REML is observed least precise in all situations. These findings are verified through a real application on test scores data, with a small value of shape parameter, and the Weibull score function turned out the most efficient.

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“…The strong consistency of β n could be established as in Bindele (2017) with slight modifications. Based on the empirical log-likelihood, a (1 − α) × 100% confidence region for β 0 is given by…”

Section: Weighted Empirical Likelihood Rank Based Inferencementioning

confidence: 99%

“…Assumptions (I 2 ) − (I 4 ) are necessary to ensure the result in Theorem 2; see Einmahl & Mason (2005), Rao (2009) and Wied & Weißbach (2012). The identifiability condition (I 5 ) is a key to ensure the strong consistency of the rank-based estimator; see Bindele (2017). Finally, assumptions (I 6 ) together with the previous assumptions are needed to establish the √ n− asymptotic normality of the proposed estimators.…”

Section: Assumptionsmentioning

confidence: 99%

Rank-based estimating equation with non-ignorable missing responses via empirical likelihood

Bindele¹,

Zhao²

2018

STAT SINICA

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In this paper, a general regression model with responses missing not at random is considered. From a rankbased estimating equation, a rank-based estimator of the regression parameter is derived. Based on this estimator's asymptotic normality property, a consistent sandwich estimator of its corresponding asymptotic covariance matrix is obtained. In order to overcome the over-coverage issue of the normal approximation procedure, the empirical likelihood based on the rank-based gradient function is defined, and its asymptotic distribution is established. Extensive simulation experiments under different settings of error distributions with different response probabilities are considered, and the simulation results show that the proposed empirical likelihood approach has better performance in terms of coverage probability and average length of confidence intervals for the regression parameters compared with the normal approximation approach and its least-squares counterpart. A real data example is provided to illustrate the proposed methods.

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Strong consistency of the general rank estimator

Cited by 8 publications

References 21 publications

Rank‐based inference with responses missing not at random

Rank‐based inference with responses missing not at random

Development of New Robust Optimal Score Function for the Weibull Distributed Error Term in Multilevel Models

Rank-based estimating equation with non-ignorable missing responses via empirical likelihood

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