A general framework of two directional simultaneous inference is provided for high-dimensional as well as the fixed dimensional models with manifest variable or latent variable structure, such as high-dimensional mean models, high- dimensional sparse regression models, and high-dimensional latent factors models. It is making the simultaneous inference on a set of parameters from two directions, one is testing whether the estimated zero parameters indeed are zero and the other is testing whether there exists zero in the parameter set of non-zero. More details can be referred to Wei Liu, et al. (2022) <doi:10.48550/arXiv.2012.11100>.
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