Efficient parameter estimation for missing data when many features are fully observed

Parameters (mean and covariance matrix) estimation is often a problem of interest since it provides information about the location and variation of the data and correlation between features and can be used for hypothesis testing, principle component analysis, etc. However, it is also common that values in some features of a dataset are missing. A popular way to deal with this problem is to use an Expectation-Maximization algorithm or to impute the missing values and then estimate the parameters based on imputed data. However, the first approach is a local optimization approach that may not converge under a fixed number of iterations. The second one, a two-step approach of imputation and analysis, is computationally inefficient. Therefore, we follow the recent trends of estimating the parameters directly from the data and propose PMF (Parameter estimation for Missing data in some Features) to deal with the aforementioned problems. The experiments show that our approach achieves better performance than other methods under comparison in performance and speed. Moreover, our estimates are asymptotic.