arXiv subjects

Jae Kwang Kim

Publications and source records attributed to Jae Kwang Kim.

At least 37 records · Page 2Linked to original sources

arXiv2023

Multiple bias-calibration for adjusting selection bias of non-probability samples using data integration

Valid statistical inference is challenging when the sample is subject to unknown selection bias. Data integration can be used to correct for selection bias when we have a parallel probability sample from the same population with some common measurements. How to model and estimate the selection probability or the propensity score (PS) of a non-probability sample using an independent probability sample is the challenging part of the data integration. We approach this difficult problem by employing multiple candidate models for PS combined with empirical likelihood. By incorporating multiple propensity score models into the internal bias calibration constraint in the empirical likelihood setup, the selection bias can be eliminated so long as the multiple candidate models contain a true PS model. The bias calibration constraint under the multiple PS models is called multiple bias calibration. Multiple PS models can include both missing-at-random and missing-not-at-random models. Asymptotic properties are discussed, and some limited simulation studies are presented to compare the proposed method with some existing competitors. Plasmode simulation studies using the Culture \& Community in a Time of Crisis dataset demonstrate the practical usage and advantages of the proposed method.

stat.ME↗

arXiv2023

An empirical likelihood approach to reduce selection bias in voluntary samples

We address the weighting problem in voluntary samples under a nonignorable sample selection model. Under the assumption that the sample selection model is correctly specified, we can compute a consistent estimator of the model parameter and construct the propensity score estimator of the population mean. We use the empirical likelihood method to construct the final weights for voluntary samples by incorporating the bias calibration constraints and the benchmarking constraints. Linearization variance estimation of the proposed method is developed. A limited simulation study is also performed to check the performance of the proposed methods.

stat.ME↗

arXiv2023

Soft calibration for selection bias problems under mixed-effects models

Calibration weighting has been widely used to correct selection biases in non-probability sampling, missing data, and causal inference. The main idea is to calibrate the biased sample to the benchmark by adjusting the subject weights. However, hard calibration can produce enormous weights when an exact calibration is enforced on a large set of extraneous covariates. This article proposes a soft calibration scheme, in which the outcome and the selection indicator follow mixed-effects models. The scheme imposes an exact calibration on the fixed effects and an approximate calibration on the random effects. On the one hand, our soft calibration has an intrinsic connection with best linear unbiased prediction, which results in a more efficient estimation compared to hard calibration. On the other hand, soft calibration weighting estimation can be envisioned as penalized propensity score weight estimation, with the penalty term motivated by the mixed-effects structure. The asymptotic distribution and a valid variance estimator are derived for soft calibration. We demonstrate the superiority of the proposed estimator over other competitors in simulation studies and a real-data application.

stat.ME↗

arXiv2022

Survey data integration for regression analysis using model calibration

We consider regression analysis in the context of data integration. To combine partial information from external sources, we employ the idea of model calibration which introduces a "working" reduced model based on the observed covariates. The working reduced model is not necessarily correctly specified but can be a useful device to incorporate the partial information from the external data. The actual implementation is based on a novel application of the information projection and model calibration weighting. The proposed method is particularly attractive for combining information from several sources with different missing patterns. The proposed method is applied to a real data example combining survey data from Korean National Health and Nutrition Examination Survey and big data from National Health Insurance Sharing Service in Korea.

stat.ME↗

arXiv2022

Maximum sampled conditional likelihood for informative subsampling

Subsampling is a computationally effective approach to extract information from massive data sets when computing resources are limited. After a subsample is taken from the full data, most available methods use an inverse probability weighted (IPW) objective function to estimate the model parameters. The IPW estimator does not fully utilize the information in the selected subsample. In this paper, we propose to use the maximum sampled conditional likelihood estimator (MSCLE) based on the sampled data. We established the asymptotic normality of the MSCLE and prove that its asymptotic variance covariance matrix is the smallest among a class of asymptotically unbiased estimators, including the IPW estimator. We further discuss the asymptotic results with the L-optimal subsampling probabilities and illustrate the estimation procedure with generalized linear models. Numerical experiments are provided to evaluate the practical performance of the proposed method.

math.ST↗

arXiv2022

Semiparametric imputation using latent sparse conditional Gaussian mixtures for multivariate mixed outcomes

This paper proposes a flexible Bayesian approach to multiple imputation using conditional Gaussian mixtures. We introduce novel shrinkage priors for covariate-dependent mixing proportions in the mixture models to automatically select the suitable number of components used in the imputation step. We develop an efficient sampling algorithm for posterior computation and multiple imputation via Markov Chain Monte Carlo methods. The proposed method can be easily extended to the situation where the data contains not only continuous variables but also discrete variables such as binary and count values. We also propose approximate Bayesian inference for parameters defined by loss functions based on posterior predictive distributing of missing observations, by extending bootstrap-based Bayesian inference for complete data. The proposed method is demonstrated through numerical studies using simulated and real data.

stat.ME↗

arXiv2022

Maximum Likelihood Imputation

Maximum likelihood (ML) estimation is widely used in statistics. The h-likelihood has been proposed as an extension of Fisher's likelihood to statistical models including unobserved latent variables of recent interest. Its advantage is that the joint maximization gives ML estimators (MLEs) of both fixed and random parameters with their standard error estimates. However, the current h-likelihood approach does not allow MLEs of variance components as Henderson's joint likelihood does not in linear mixed models. In this paper, we show how to form the h-likelihood in order to facilitate joint maximization for MLEs of whole parameters. We also show the role of the Jacobian term which allows MLEs in the presence of unobserved latent variables. To obtain MLEs for fixed parameters, intractable integration is not necessary. As an illustration, we show one-shot ML imputation for missing data by treating them as realized but unobserved random parameters. We show that the h-likelihood bypasses the expectation step in the expectation-maximization (EM) algorithm and allows single ML imputation instead of multiple imputations. We also discuss the difference in predictions in random effects and missing data.

stat.ME↗

arXiv2022

Information projection approach to propensity score estimation for handling selection bias under missing at random

Propensity score weighting is widely used to improve the representativeness and correct the selection bias in the voluntary sample. The propensity score is often developed using a model for the sampling probability, which can be subject to model misspecification. In this paper, we consider an alternative approach of estimating the inverse of the propensity scores using the density ratio function satisfying the self-efficiency condition. The smoothed density ratio function is obtained by the solution to the information projection onto the space satisfying the moment conditions on the balancing scores. By including the covariates for the outcome regression models only in the density ratio model, we can achieve efficient propensity score estimation. Penalized regression is used to identify important covariates. We further extend the proposed approach to the multivariate missing case. Some limited simulation studies are presented to compare with the existing methods.

stat.ME↗

arXiv2022

Functional Calibration under Non-Probability Survey Sampling

Non-probability sampling is prevailing in survey sampling, but ignoring its selection bias leads to erroneous inferences. We offer a unified nonparametric calibration method to estimate the sampling weights for a non-probability sample by calibrating functions of auxiliary variables in a reproducing kernel Hilbert space. The consistency and the limiting distribution of the proposed estimator are established, and the corresponding variance estimator is also investigated. Compared with existing works, the proposed method is more robust since no parametric assumption is made for the selection mechanism of the non-probability sample. Numerical results demonstrate that the proposed method outperforms its competitors, especially when the model is misspecified. The proposed method is applied to analyze the average total cholesterol of Korean citizens based on a non-probability sample from the National Health Insurance Sharing Service and a reference probability sample from the Korea National Health and Nutrition Examination Survey.

stat.ME↗

arXiv2022

Nearest neighbor ratio imputation with incomplete multi-nomial outcome in survey sampling

Nonresponse is a common problem in survey sampling. Appropriate treatment can be challenging, especially when dealing with detailed breakdowns of totals. Often, the nearest neighbor imputation method is used to handle such incomplete multinomial data. In this article, we investigate the nearest neighbor ratio imputation estimator, in which auxiliary variables are used to identify the closest donor and the vector of proportions from the donor is applied to the total of the recipient to implement ratio imputation. To estimate the asymptotic variance, we first treat the nearest neighbor ratio imputation as a special case of predictive matching imputation and apply the linearization method of \cite{yang2020asymptotic}. To account for the non-negligible sampling fractions, parametric and generalized additive models are employed to incorporate the smoothness of the imputation estimator, which results in a valid variance estimator. We apply the proposed method to estimate expenditures detail items based on empirical data from the 2018 collection of the Service Annual Survey, conducted by the United States Census Bureau. Our simulation results demonstrate the validity of our proposed estimators and also confirm that the derived variance estimators have good performance even when the sampling fraction is non-negligible.

stat.ME↗

arXiv2021

Statistical inference using Regularized M-estimation in the reproducing kernel Hilbert space for handling missing data

Imputation and propensity score weighting are two popular techniques for handling missing data. We address these problems using the regularized M-estimation techniques in the reproducing kernel Hilbert space. Specifically, we first use the kernel ridge regression to develop imputation for handling item nonresponse. While this nonparametric approach is potentially promising for imputation, its statistical properties are not investigated in the literature. Under some conditions on the order of the tuning parameter, we first establish the root-$n$ consistency of the kernel ridge regression imputation estimator and show that it achieves the lower bound of the semiparametric asymptotic variance. A nonparametric propensity score estimator using the reproducing kernel Hilbert space is also developed by a novel application of the maximum entropy method for the density ratio function estimation. We show that the resulting propensity score estimator is asymptotically equivalent to the kernel ridge regression imputation estimator. Results from a limited simulation study are also presented to confirm our theory. The proposed method is applied to analyze the air pollution data measured in Beijing, China.

stat.ME↗

arXiv2020

Combining Non-probability and Probability Survey Samples Through Mass Imputation

This paper presents theoretical results on combining non-probability and probability survey samples through mass imputation, an approach originally proposed by Rivers (2007) as sample matching without rigorous theoretical justification. Under suitable regularity conditions, we establish the consistency of the mass imputation estimator and derive its asymptotic variance formula. Variance estimators are developed using either linearization or bootstrap. Finite sample performances of the mass imputation estimator are investigated through simulation studies and an application to analyzing a non-probability sample collected by the Pew Research Centre.

stat.ME↗

arXiv2020

Imputation estimators for unnormalized models with missing data

Several statistical models are given in the form of unnormalized densities, and calculation of the normalization constant is intractable. We propose estimation methods for such unnormalized models with missing data. The key concept is to combine imputation techniques with estimators for unnormalized models including noise contrastive estimation and score matching. In addition, we derive asymptotic distributions of the proposed estimators and construct confidence intervals. Simulation results with truncated Gaussian graphical models and the application to real data of wind direction reveal that the proposed methods effectively enable statistical inference with unnormalized models from missing data.

stat.ML↗

arXiv2020

Semiparametric Optimal Estimation With Nonignorable Nonresponse Data

When the response mechanism is believed to be not missing at random (NMAR), a valid analysis requires stronger assumptions on the response mechanism than standard statistical methods would otherwise require. Semiparametric estimators have been developed under the model assumptions on the response mechanism. In this paper, a new statistical test is proposed to guarantee model identifiability without using any instrumental variable. Furthermore, we develop optimal semiparametric estimation for parameters such as the population mean. Specifically, we propose two semiparametric optimal estimators that do not require any model assumptions other than the response mechanism. Asymptotic properties of the proposed estimators are discussed. An extensive simulation study is presented to compare with some existing methods. We present an application of our method using Korean Labor and Income Panel Survey data.

stat.ME↗

arXiv2020

An Approximate Bayesian Approach to Model-assisted Survey Estimation with Many Auxiliary Variables

Model-assisted estimation with complex survey data is an important practical problem in survey sampling. When there are many auxiliary variables, selecting significant variables associated with the study variable would be necessary to achieve efficient estimation of population parameters of interest. In this paper, we formulate a regularized regression estimator in the framework of Bayesian inference using the penalty function as the shrinkage prior for model selection. The proposed Bayesian approach enables us to get not only efficient point estimates but also reasonable credible intervals. Results from two limited simulation studies are presented to facilitate comparison with existing frequentist methods.

stat.ME↗

arXiv2020

Statistical Data Integration in Survey Sampling: A Review

Finite population inference is a central goal in survey sampling. Probability sampling is the main statistical approach to finite population inference. Challenges arise due to high cost and increasing non-response rates. Data integration provides a timely solution by leveraging multiple data sources to provide more robust and efficient inference than using any single data source alone. The technique for data integration varies depending on types of samples and available information to be combined. This article provides a systematic review of data integration techniques for combining probability samples, probability and non-probability samples, and probability and big data samples. We discuss a wide range of integration methods such as generalized least squares, calibration weighting, inverse probability weighting, mass imputation and doubly robust methods. Finally, we highlight important questions for future research.

stat.ME↗

arXiv2019

Semiparametric Imputation Using Conditional Gaussian Mixture Models under Item Nonresponse

Imputation is a popular technique for handling item nonresponse in survey sampling. Parametric imputation is based on a parametric model for imputation and is less robust against the failure of the imputation model. Nonparametric imputation is fully robust but is not applicable when the dimension of covariates is large due to the curse of dimensionality. Semiparametric imputation is another robust imputation based on a flexible model where the number of model parameters can increase with the sample size. In this paper, we propose another semiparametric imputation based on a more flexible model assumption than the Gaussian mixture model. In the proposed mixture model, we assume a conditional Gaussian model for the study variable given the auxiliary variables, but the marginal distribution of the auxiliary variables is not necessarily Gaussian. We show that the proposed mixture model achieves a lower approximation error bound to any unknown target density than the Gaussian mixture model in terms of the Kullback-Leibler divergence. The proposed method is applicable to high dimensional covariate problem by including a penalty function in the conditional log-likelihood function. The proposed method is applied to 2017 Korean Household Income and Expenditure Survey conducted by Statistics Korea. Supplementary material is available online.

stat.ME↗

arXiv2019

Doubly Robust Inference when Combining Probability and Non-probability Samples with High-dimensional Data

Non-probability samples become increasingly popular in survey statistics but may suffer from selection biases that limit the generalizability of results to the target population. We consider integrating a non-probability sample with a probability sample which provides high-dimensional representative covariate information of the target population. We propose a two-step approach for variable selection and finite population inference. In the first step, we use penalized estimating equations with folded-concave penalties to select important variables for the sampling score of selection into the non-probability sample and the outcome model. We show that the penalized estimating equation approach enjoys the selection consistency property for general probability samples. The major technical hurdle is due to the possible dependence of the sample under the finite population framework. To overcome this challenge, we construct martingales which enable us to apply Bernstein concentration inequality for martingales. In the second step, we focus on a doubly robust estimator of the finite population mean and re-estimate the nuisance model parameters by minimizing the asymptotic squared bias of the doubly robust estimator. This estimating strategy mitigates the possible first-step selection error and renders the doubly robust estimator root-n consistent if either the sampling probability or the outcome model is correctly specified.

stat.ME↗