Copula-Based Analysis of Dependent Data with Censoring and Zero Inflation Open Access
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The analysis of time series data with detection limits is challenging due to the high-dimensional integral involved in the likelihood. To account for the computational challenge, various methods have been developed but most of them rely on restrictive parametric distributional assumptions. In the first porject, we propose a semiparametric method for analyzing censored time series, where the temporal dependence is captured by parametric copula while the marginal distributions are estimated nonparametrically. Utilizing the properties of copula modeling, 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 easily 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 it leads to more accurate predictions than Gaussian-based methods for non-normal data. In the second project, we focus on the analysis of multi-site precipitation data that are zero-inflated. We consider an alternative three-part copula-based model to analyze precipitations at multiple locations, where copula functions are used to capture the dependence among locations, and the marginal distribution is characterized through the first two parts of the model.