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Abstract:
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Times series data, especially those arising from environmental, biomedical and social studies, are frequently censored due to detection limits of the monitoring device or top/bottom coding. Censoring caused by detection limits complicates the time series data analysis in two major ways. Firstly, the likelihood involves multi-dimensional integral with the dimension as large as the number of censored observations. Secondly, under censoring, the model parameters are often nonidentifiable without parametric distributional assumptions. In this paper, we propose a new semiparametric copula-based estimation method for stationary Markov models with detection limits. The idea of copula was also considered by Chen and Fan (2006) and Chen et al. (2009) but they focused on Markov models with fully observed data. In our proposed method, the marginal distribution is left unspecified and estimated non-parametrically, and the copula function can be chosen from a class of parametric copula functions. Our theoretical derivation, simulation results and real data analysis all suggest that the proposed method leads to unbiased and more efficient estimation than the naive approaches.
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