In our paper, we focus on robust variable selection for missing data and measurement error.Missing data and measurement errors can lead to confusing data distribution.We propose an exponential loss function with tuning parameter to apply to Missing and measurement errors data.By adjusting the parameter,the loss function can be better and more robust under various different data distributions.We use inverse probability weighting and additivity error models to address missing data and measurement errors. Also, we find that the Atan punishment method works better.We used Monte Carlo simulations to assess the validity of robust variable selection and validated our findings with the breast cancer dataset

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