arXiv subjects

Jae Kwang Kim

Publications and source records attributed to Jae Kwang Kim.

50 records · Page 3Linked to original sources

arXiv2019

Bootstrap inference for the finite population total under complex sampling designs

Bootstrap is a useful tool for making statistical inference, but it may provide erroneous results under complex survey sampling. Most studies about bootstrap-based inference are developed under simple random sampling and stratified random sampling. In this paper, we propose a unified bootstrap method applicable to some complex sampling designs, including Poisson sampling and probability-proportional-to-size sampling. Two main features of the proposed bootstrap method are that studentization is used to make inference, and the finite population is bootstrapped based on a multinomial distribution by incorporating the sampling information. We show that the proposed bootstrap method is second-order accurate using the Edgeworth expansion. Two simulation studies are conducted to compare the proposed bootstrap method with the Wald-type method, which is widely used in survey sampling. Results show that the proposed bootstrap method is better in terms of coverage rate especially when sample size is limited.

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arXiv2018

Accounting for model uncertainty in multiple imputation under complex sampling

Multiple imputation provides an effective way to handle missing data. When several possible models are under consideration for the data, the multiple imputation is typically performed under a single-best model selected from the candidate models. This single model selection approach ignores the uncertainty associated with the model selection and so leads to underestimation of the variance of multiple imputation estimator. In this paper, we propose a new multiple imputation procedure incorporating model uncertainty in the final inference. The proposed method incorporates possible candidate models for the data into the imputation procedure using the idea of Bayesian Model Averaging (BMA). The proposed method is directly applicable to handling item nonresponse in survey sampling. Asymptotic properties of the proposed method are investigated. A limited simulation study confirms that our model averaging approach provides better estimation performance than the single model selection approach.

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arXiv2018

Semiparametric response model with nonignorable nonresponse

How to deal with nonignorable response is often a challenging problem encountered in statistical analysis with missing data. Parametric model assumption for the response mechanism is often made and there is no way to validate the model assumption with missing data. We consider a semiparametric response model that relaxes the parametric model assumption in the response mechanism. Two types of efficient estimators, profile maximum likelihood estimator and profile calibration estimator, are proposed and their asymptotic properties are investigated. Two extensive simulation studies are used to compare with some existing methods. We present an application of our method using Korean Labor and Income Panel Survey data.

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arXiv2018

Semiparametric fractional imputation using Gaussian mixture models for handling multivariate missing data

Item nonresponse is frequently encountered in practice. Ignoring missing data can lose efficiency and lead to misleading inference. Fractional imputation is a frequentist approach of imputation for handling missing data. However, the parametric fractional imputation of \cite{kim2011parametric} may be subject to bias under model misspecification. In this paper, we propose a novel semiparametric fractional imputation method using Gaussian mixture models. The proposed method is computationally efficient and leads to robust estimation. The proposed method is further extended to incorporate the categorical auxiliary information. The asymptotic model consistency and $\sqrt{n}$- consistency of the semiparametric fractional imputation estimator are also established. Some simulation studies are presented to check the finite sample performance of the proposed method.

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arXiv2018

Bayesian Sparse Propensity Score Estimation for Unit Nonresponse

Nonresponse weighting adjustment using propensity score is a popular method for handling unit nonresponse. However, including all available auxiliary variables into the propensity model can lead to inefficient and inconsistent estimation, especially with high-dimensional covariates. In this paper, a new Bayesian method using the Spike-and-Slab prior is proposed for sparse propensity score estimation. The proposed method is not based on any model assumption on the outcome variable and is computationally efficient. Instead of doing model selection and parameter estimation separately as in many frequentist methods, the proposed method simultaneously selects the sparse response probability model and provides consistent parameter estimation. Some asymptotic properties of the proposed method are presented. The efficiency of this sparse propensity score estimator is further improved by incorporating related auxiliary variables from the full sample. The finite-sample performance of the proposed method is investigated in two limited simulation studies, including a partially simulated real data example from the Korean Labor and Income Panel Survey.

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arXiv2018

Integration of survey data and big observational data for finite population inference using mass imputation

Multiple data sources are becoming increasingly available for statistical analyses in the era of big data. As an important example in finite-population inference, we consider an imputation approach to combining a probability sample with big observational data. Unlike the usual imputation for missing data analysis, we create imputed values for the whole elements in the probability sample. Such mass imputation is attractive in the context of survey data integration (Kim and Rao, 2012). We extend mass imputation as a tool for data integration of survey data and big non-survey data. The mass imputation methods and their statistical properties are presented. The matching estimator of Rivers (2007) is also covered as a special case. Variance estimation with mass-imputed data is discussed. The simulation results demonstrate the proposed estimators outperform existing competitors in terms of robustness and efficiency.

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arXiv2018

Sampling techniques for big data analysis in finite population inference

In analyzing big data for finite population inference, it is critical to adjust for the selection bias in the big data. In this paper, we propose two methods of reducing the selection bias associated with the big data sample. The first method uses a version of inverse sampling by incorporating auxiliary information from external sources, and the second one borrows the idea of data integration by combining the big data sample with an independent probability sample. Two simulation studies show that the proposed methods are unbiased and have better coverage rates than their alternatives. In addition, the proposed methods are easy to implement in practice.

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arXiv2018

Predictive mean matching imputation in survey sampling

Predictive mean matching imputation is popular for handling item nonresponse in survey sampling. In this article, we study the asymptotic properties of the predictive mean matching estimator of the population mean. For variance estimation, the conventional bootstrap inference for matching estimators with fixed matches has been shown to be invalid due to the nonsmoothness nature of the matching estimator. We propose asymptotically valid replication variance estimation. The key strategy is to construct replicates of the estimator directly based on linear terms, instead of individual records of variables. Extension to nearest neighbor imputation is also discussed. A simulation study confirms that the new procedure provides valid variance estimation.

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arXiv2017

Nearest neighbor imputation for general parameter estimation in survey sampling

Nearest neighbor imputation is popular for handling item nonresponse in survey sampling. In this article, we study the asymptotic properties of the nearest neighbor imputation estimator for general population parameters, including population means, proportions and quantiles. For variance estimation, the conventional bootstrap inference for matching estimators with fixed number of matches has been shown to be invalid due to the nonsmoothness nature of the matching estimator. We propose asymptotically valid replication variance estimation. The key strategy is to construct replicates of the estimator directly based on linear terms, instead of individual records of variables. A simulation study confirms that the new procedure provides valid variance estimation.

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arXiv2017

An approximate Bayesian inference on propensity score estimation under unit nonresponse

Nonresponse weighting adjustment using the response propensity score is a popular tool for handling unit nonresponse. Statistical inference after the nonresponse weighting adjustment is complicated because the effect of estimating the propensity model parameter needs to be incorporated. In this paper, we propose an approximate Bayesian approach to handle unit nonresponse with parametric model assumptions on the response probability, but without model assumptions for the outcome variable. The proposed Bayesian method is calibrated to the frequentist inference in that the credible region obtained from the posterior distribution asymptotically matches to the frequentist confidence interval obtained from the Taylor linearization method. Unlike the frequentist approach, however, the proposed method does not involve Taylor linearization. The proposed method can be extended to handle over-identified cases in which there are more estimating equations than the parameters. Besides, the proposed method can also be modified to handle nonignorable nonresponse. Results from two simulation studies confirm the validity of the proposed methods, which are then applied to data from a Korean longitudinal survey.

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arXiv2015

A note on multiple imputation for method of moments estimation

Multiple imputation is a popular imputation method for general purpose estimation. Rubin(1987) provided an easily applicable formula for the variance estimation of multiple imputation. However, the validity of the multiple imputation inference requires the congeniality condition of Meng(1994), which is not necessarily satisfied for method of moments estimation. This paper presents the asymptotic bias of Rubin's variance estimator when the method of moments estimator is used as a complete-sample estimator in the multiple imputation procedure. A new variance estimator based on over-imputation is proposed to provide asymptotically valid inference for method of moments estimation.

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arXiv2015

Fractional Imputation in Survey Sampling: A Comparative Review

Fractional imputation (FI) is a relatively new method of imputation for handling item nonresponse in survey sampling. In FI, several imputed values with their fractional weights are created for each missing item. Each fractional weight represents the conditional probability of the imputed value given the observed data, and the parameters in the conditional probabilities are often computed by an iterative method such as EM algorithm. The underlying model for FI can be fully parametric, semiparametric, or nonparametric, depending on plausibility of assumptions and the data structure. In this paper, we give an overview of FI, introduce key ideas and methods to readers who are new to the FI literature, and highlight some new development. We also provide guidance on practical implementation of FI and valid inferential tools after imputation. We demonstrate the empirical performance of FI with respect to multiple imputation using a pseudo finite population generated from a sample in Monthly Retail Trade Survey in US Census Bureau.

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arXiv2011

Variance estimation for nearest neighbor imputation for US Census long form data

Variance estimation for estimators of state, county, and school district quantities derived from the Census 2000 long form are discussed. The variance estimator must account for (1) uncertainty due to imputation, and (2) raking to census population controls. An imputation procedure that imputes more than one value for each missing item using donors that are neighbors is described and the procedure using two nearest neighbors is applied to the Census long form. The Kim and Fuller [Biometrika 91 (2004) 559--578] method for variance estimation under fractional hot deck imputation is adapted for application to the long form data. Numerical results from the 2000 long form data are presented.

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arXiv2004

Finite sample properties of multiple imputation estimators

Finite sample properties of multiple imputation estimators under the linear regression model are studied. The exact bias of the multiple imputation variance estimator is presented. A method of reducing the bias is presented and simulation is used to make comparisons. We also show that the suggested method can be used for a general class of linear estimators.

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