Homogeneity detection for the high-dimensional generalized linear model

We propose to use a penalized estimator for detecting homogeneity of the high-dimensional generalized linear model. Here, the homogeneity is a specific model structure where regression coefficients are grouped having exactly the same value in each group. The proposed estimator achieves weak oracle property under mild regularity conditions and is invariant to the choice of reference levels when there are categorical covariates in the model. An efficient algorithm is also provided. Various numerical studies confirm that the proposed penalized estimator gives better performance than other conventional variable selection estimators when the model has homogeneity.