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Long-tail and skewed data are frequently encountered in both economics and health-care fields. Since the data on the distribution tail are scarce yet very important, inappropriately handling of such data can lead to unstable and biased estimation results. We have developed a series of methods to analyze such data. Particularly, we developed a method to estimate the transformation function and error distribution function so to avoid the difficulty of specifying these functions in modeling. In addition, invoking jointly the smoothing technology, penalty and rank correlation, we have developed a new dimension-free calculation method to quickly select the important risk factors from a large number of potential risk factors. Furthermore, we proposed a semi-parametric latent transformation model to combine multiple skewed and long-tail outcomes in a data-driven way. The analysis of real data showed that our methods are more efficient and robust than the existing methods to identify influential risk factors.

Nonparametric Estimation on Regression Coefficient and Population Size for Incomplete or Skewed Data