Use of redundant statistical model is often the case with practical data analysis. Redundancy widely investigated is inclusion of irrelevant predictors which is resolved by setting their coefficients to zero. On the other hand, it is also useful to consider overlapping parameters of which the values are similar. Grouping by regarding a set of parameters as a single parameter contributes to building intimate parameterization and increasing estimation accuracy by dimension reduction.
The paper proposes a data adaptive automatic grouping of parameters, which simultaneously enables variable selection that can yield sparse solution, by applying the smooth-thresholding. The new procedure is applicable to several estimation equation-based methods, and is shown to possess the oracle property. No convex optimization is needed for its implementation. Numerical examinations including large p small n situation are performed. Proposed automatic grouping applies to interaction modeling for Ohio wheeze data and for credit scoring data.
"Automatic grouping using smooth-threshold estimating equations." Electron. J. Statist. 5 309 - 328, 2011. https://doi.org/10.1214/11-EJS608