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- Title
Copula‐based semiparametric analysis for time series data with detection limits.
- Authors
Li, Fuyuan; Tang, Yanlin; Wang, Huixia Judy
- 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 Statistics 47: 438–454; 2019 © 2019 Statistical Society of Canada
- Subjects
CANADA; TIME series analysis; DETECTION limit; MARGINAL distributions; WATER quality; WATER analysis; DEPENDENCE (Statistics); BIVARIATE analysis
- Publication
Canadian Journal of Statistics, 2019, Vol 47, Issue 3, p438
- ISSN
0319-5724
- Publication type
Article
- DOI
10.1002/cjs.11503