Imputation methods for quantile estimation under missing at random

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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“…Yang et al . () proposed a fractional hot deck imputation based on non‐parametric kernel regression.…”

Section: Introductionmentioning

confidence: 99%

“…Estimating equations were used by Wei and Yang (2014) to produce consistent linear quantile estimation in the presence of missing covariates through an expectation-maximization type of algorithm. Yang et al (2013) proposed a fractional hot deck imputation based on non-parametric kernel regression.…”

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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“…where predicted values g n (X i ) are combined with residuals u j to emulate a pseudo-sample of responses Y ij , as suggested by equation (15). Sued and Yohai [20], proposed a semiparametric regression model for (15), where the regression function is assumed to be in a parametric family: g(X) = g(X; β 0 ), with β 0 ∈ B ⊂ R q , and g : R p × B → R is a known function. No other than a centrality condition, namely symmetry around zero, is imposed on the error term u.…”

Section: Regression Estimators Of Fmentioning

confidence: 99%

“…Cheng and Chu [14], proposed a Nadaraya-Watson estimator for the conditional distribution of Y given X and used it to derive a non parametric estimator for the distribution function F 0 . Yang, Kim and Shin [15] presented an imputation method for estimating the quantiles. Imputed data sets are constructed generating plausible values to represent the uncertainty about missing responses.…”

Section: Introductionmentioning

confidence: 99%

Robust Doubly Protected Estimators for Quantiles with Missing Data

Molina¹,

Sued²,

Valdora³

et al. 2017

Preprint

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Doubly protected methods are widely used for estimating the population mean of an outcome Y from a sample where the response is missing in some individuals. To compensate for the missing responses, a vector X of covariates is observed at each individual, and the missing mechanism is assumed to be independent of the response, conditioned on X (missing at random). In recent years, many authors have turned from the estimation of the mean to that of the median, and more generally, doubly protected estimators of the quantiles have been proposed, under a parametric regression model for the relationship between X and Y and a parametric form for the propensity score. In this work, we present doubly protected estimators for the quantiles that are also robust, in the sense that they are resistant to the presence of outliers in the sample. We also flexibilize the model for the relationship between X and Y . Thus we present robust doubly protected estimators for the quantiles of the response in the presence of missing observations, postulating a semiparametric regression model for the relationship between the response and the covariates and a parametric model for the propensity score.

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“…Chen [4] discussed efficient QR analysis with missing observations. Shu [15] proposed some imputation methods for quantile estimation under missing at random.…”

Section: Introductionmentioning

confidence: 99%

Empirical likelihood for quantile regression models with response data missing at random

Luo

Pang

2017

Open Mathematics

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This paper studies quantile linear regression models with response data missing at random. A quantile empirical-likelihood-based method is proposed firstly to study a quantile linear regression model with response data missing at random. It follows that a class of quantile empirical log-likelihood ratios including quantile empirical likelihood ratio with complete-case data, weighted quantile empirical likelihood ratio and imputed quantile empirical likelihood ratio are defined for the regression parameters. Then, a bias-corrected quantile empirical log-likelihood ratio is constructed for the mean of the response variable for a given quantile level. It is proved that these quantile empirical log-likelihood ratios are asymptotically 2 distribution. Furthermore, a class of estimators for the regression parameters and the mean of the response variable are constructed, and the asymptotic normality of the proposed estimators is established. Our results can be used directly to construct the confidence intervals (regions) of the regression parameters and the mean of the response variable. Finally, simulation studies are conducted to assess the finite sample performance and a real-world data set is analyzed to illustrate the applications of the proposed method.

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Imputation methods for quantile estimation under missing at random

Cited by 8 publications

References 11 publications

A General Framework for Quantile Estimation with Incomplete Data

A General Framework for Quantile Estimation with Incomplete Data

Robust Doubly Protected Estimators for Quantiles with Missing Data

Empirical likelihood for quantile regression models with response data missing at random

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