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Abstract:
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In recent years, many efforts have been made in the field of high-dimensional inference. We propose an intuitive and computationally efficient procedure to carry out inference for high-dimensional MCP-penalized linear models. The KKT conditions for MCP allow inference to be carried out using an approximate projection onto the column space of the active features. We show that this approach, PIPE (Projection Inference using Penalized regression Estimators), can be used to construct confidence intervals and false discovery rates for MCP estimates. We conducted simulations to study PIPE’s empirical performance at finite sample size and compare the approach to existing high-dimensional inference methods. Finally, we consider the potential of extending this idea to estimates arising from penalized regression models using the LASSO.
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