Robust estimation of distribution functions and quantiles with non‐ignorable missing data

Zhao, Pu Ying; Tang, Man Lai; Tang, Nian

doi:10.1002/cjs.11195

Cited by 14 publications

(7 citation statements)

References 32 publications

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“…Under a non‐ignorable missingness mechanism, Zhao et al . () proposed an augmented IPW method to estimate the distribution function and quantiles of a response variable. Sun et al .…”

Section: Introductionmentioning

confidence: 99%

A General Framework for Quantile Estimation with Incomplete Data

Han

Kong

Zhao

et al. 2019

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Summary Quantile estimation has attracted significant research interest in recent years. However, there has been only a limited literature on quantile estimation in the presence of incomplete data. We propose a general framework to address this problem. Our framework combines the two widely adopted approaches for missing data analysis, the imputation approach and the inverse probability weighting approach, via the empirical likelihood method. The method proposed is capable of dealing with many different missingness settings. We mainly study three of them: estimating the marginal quantile of a response that is subject to missingness while there are fully observed covariates; estimating the conditional quantile of a fully observed response while the covariates are partially available; estimating the conditional quantile of a response that is subject to missingness with fully observed covariates and extra auxiliary variables. The method proposed allows multiple models for both the missingness probability and the data distribution. The resulting estimators are multiply robust in the sense that they are consistent if any one of these models is correctly specified. The asymptotic distributions are established by using empirical process theory.

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“…Under a non‐ignorable missingness mechanism, Zhao et al . () proposed an augmented IPW method to estimate the distribution function and quantiles of a response variable. Sun et al .…”

Section: Introductionmentioning

confidence: 99%

A General Framework for Quantile Estimation with Incomplete Data

Han

Kong

Zhao

et al. 2019

Journal of the Royal Statistical Society Series B: Statistical Methodology

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“…It is challenging to undertake statistical inference on nonignorable missing data because the missingness data mechanism depends on missing variables (Zhao, Tang & Tang, 2013a, 2013bTang & Tang, 2018). In this vein, Kim & Yu (2011) considered an exponential tilting model for the probability that a response is observed and proposed a semiparametric method to estimate the mean function in the presence of nonignorable missing responses.…”

Section: Introductionmentioning

confidence: 99%

“…In this vein, Kim & Yu (2011) considered an exponential tilting model for the probability that a response is observed and proposed a semiparametric method to estimate the mean function in the presence of nonignorable missing responses. Likewise, Zhao, Zhao & Tang (2013a, 2013b utilized the EL method to investigate the problem of estimating mean functionals with or without using auxiliary information in the presence of nonignorable missing responses. Tang, Zhao & Zhu (2014) developed a method of EL inference for parameters in generalized EEs with nonignorabe missing data.…”

Section: Introductionmentioning

confidence: 99%

Empirical likelihood for nonlinear regression models with nonignorable missing responses

Yang

Tang

2020

Can J Statistics

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This article develops three empirical likelihood (EL) approaches to estimate parameters in nonlinear regression models in the presence of nonignorable missing responses. These are based on the inverse probability weighted (IPW) method, the augmented IPW (AIPW) method and the imputation technique. A logistic regression model is adopted to specify the propensity score. Maximum likelihood estimation is used to estimate parameters in the propensity score by combining the idea of importance sampling and imputing estimating equations. Under some regularity conditions, we obtain the asymptotic properties of the maximum EL estimators of these unknown parameters. Simulation studies are conducted to investigate the finite sample performance of our proposed estimation procedures. Empirical results provide evidence that the AIPW procedure exhibits better performance than the other two procedures. Data from a survey conducted in 2002 are used to illustrate the proposed estimation procedure. The Canadian Journal of Statistics 48: 386–416; 2020 © 2020 Statistical Society of Canada

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“…Okafor and Lee [8] presented ratio and regression estimation with partial sampling of the nonrespondents for estimating the population mean. Furthermore, the authors of [9,10] proposed estimators for estimating population mean using multiauxiliary information in different directions and Zhao et al [11] used the idea of robust estimation of the distribution function and quantiles with nonignorance missing data.…”

Section: Introductionmentioning

confidence: 99%

On Estimation of Distribution Function Using Dual Auxiliary Information under Nonresponse Using Simple Random Sampling

Hussain

et al. 2020

Journal of Probability and Statistics

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In this paper, we proposed two new families of estimators using the supplementary information on the auxiliary variable and exponential function for the population distribution functions in case of nonresponse under simple random sampling. The estimations are done in two nonresponse scenarios. These are nonresponse on study variable and nonresponse on both study and auxiliary variables. As we have highlighted above that two new families of estimators are proposed, in the first family, the mean was used, while in the second family, ranks were used as auxiliary variables. Expression of biases and mean squared error of the proposed and existing estimators are obtained up to the first order of approximation. The performances of the proposed and existing estimators are compared theoretically. On these theoretical comparisons, we demonstrate that the proposed families of estimators are better in performance than the existing estimators available in the literature, under the obtained conditions. Furthermore, these theoretical findings are braced numerically by an empirical study offering the proposed relative efficiencies of the proposed families of estimators.

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Robust estimation of distribution functions and quantiles with non‐ignorable missing data

Cited by 14 publications

References 32 publications

A General Framework for Quantile Estimation with Incomplete Data

A General Framework for Quantile Estimation with Incomplete Data

Empirical likelihood for nonlinear regression models with nonignorable missing responses

On Estimation of Distribution Function Using Dual Auxiliary Information under Nonresponse Using Simple Random Sampling

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