Poisson regression with error corrupted high dimensional features

Features extracted from aggregated data are often contaminated with errors. Errors in these features are usually difficult to handle, especially when the feature dimension is high. We construct an estimator of the feature effects in the context of a Poisson regression with a high dimensional feature and additive measurement errors. The procedure penalizes a target function that is specially designed to handle measurement errors. We perform optimization within a bounded region. Benefiting from the convexity of the constructed target function in this region, we establish the theoretical properties of the new estimator in terms of algorithmic convergence and statistical consistency. The numerical performance is demonstrated using simulation studies. We apply the method to analyze the possible effect of weather on the number of COVID-19 cases.