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Abstract The analysis of time series data with detection limits is challenging due to the high‐dimensional integral involved in the likelihood. Existing methods are either computationally demanding or rely on restrictive parametric distributional assumptions. We propose a semiparametric approach, where the temporal dependence is captured by parametric copula, while the marginal distribution is estimated non‐parametrically. Utilizing the properties of copulas, we develop a new copula‐based sequential sampling algorithm, which provides a convenient way to calculate the censored likelihood. Even without full parametric distributional assumptions, the proposed method still allows us to efficiently compute the conditional quantiles of the censored response at a future time point, and thus construct both point and interval predictions. We establish the asymptotic properties of the proposed pseudo maximum likelihood estimator, and demonstrate through simulation and the analysis of a water quality data that the proposed method is more flexible and leads to more accurate predictions than Gaussian‐based methods for non‐normal data.The Canadian Journal of Statistics47: 438–454; 2019 © 2019 Statistical Society of Canada
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Semiparametric imputation using conditional Gaussian mixture models under item nonresponse
Abstract Imputation is a popular technique for handling item nonresponse. Parametric imputation is based on a parametric model for imputation and is not 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 a new 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. The proposed mixture model is more flexible and achieves a better approximation than the Gaussian mixture models. 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 the 2017 Korean Household Income and Expenditure Survey conducted by Statistics Korea.
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- PAR ID:
- 10364514
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Biometrics
- Volume:
- 78
- Issue:
- 1
- ISSN:
- 0006-341X
- Format(s):
- Medium: X Size: p. 227-237
- Size(s):
- p. 227-237
- Sponsoring Org:
- National Science Foundation
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