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This paper considers the estimation of regression models when data is collected in a stratified mode using a categorical variable. This kind of data appears in fields frequently since data is collected from various sources. Most of the literature analyzes the data assuming that the stratified information is known, while this information is not always attainable. In this paper, we assume the stratified information is unknown. The proposed joint estimation combines the clustering technique and penalized regression modeling, so that it can be applied to high-dimensional stratified data without specific information. We show that the proposed method enjoys asymptotic properties. Simulations and empirical studies confirm that our method outperforms the methods without stratification. We apply the proposed method to gene expression data and temperature data, obtaining some meaningful results.

A joint estimation for the high-dimensional regression modeling on stratified data