High-dimensional data is more easer to collect in the big-data age. This talk investigates the statistical modeling and testing for high-dimensional data. First, we develop Fabs algorithms, a computationally cheaper algorithm, to solve lasso-based problem, as well as tensor-decomposition-based methods for multivariate high-dimensional additive-models. Second, we provide novel methods to construct efficient confidence intervals for treatment effects in high-dimensional setting. Third, we propose the test statistics for high-dimensional group testing problem, including the cases when the high or low-dimensional nuisance parameter presents.
