A Semi-Parametric Mixture Model for Left-Censored and Zero-Inflated Data, with Application to Environment

M. Pereda Vivo, C. Paroissin

First, we propose a new semi-parametric mixture model for dealing with left-censored zero-inflated data. This model appears to offer an alternative to previous approaches. In particular, we consider a proportional reversed hazard rate model for the positive part and a logistic model for the probability of a zero response, both of which include the effect of covariates. We obtain parameter estimates and we derive the asymptotic properties of the proposed estimators.

We then apply the model to a real dataset relating to arsenic concentration in water in Bangladesh. This dataset comprises 3,534 groundwater samples from tube wells, nearly 30% of which are left-censored.
The analysis includes several covariates, such as well depth, geographical location, well type and temperature. We fitted the proposed mixture model. This enables us to interpret the impact of these covariates on the distribution of arsenic concentrations.

Keywords: Left-censoring, Reversed hazard rate, Semi-parametric models , Zero inflation

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