Estimation and clustering for partially heterogeneous single index model

Fangfang Wang, Lu Lin (), Lei Liu and Kangning Wang
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Fangfang Wang: Shandong University
Lu Lin: Shandong Technology and Business University
Lei Liu: Washington University in St. Louis
Kangning Wang: Shandong Technology and Business University

Statistical Papers, 2021, vol. 62, issue 6, No 2, 2529-2556

Abstract: Abstract In this paper, our goal is to estimate the homogeneous parameter and cluster the heterogeneous parameters in a partially heterogeneous single index model (PHSIM). To achieve the goal, the minimization criterion for such a single index model is first transformed into a least-squares optimization problem in the population form. Based on the least-squares objective function, we introduce an empirical version for the PHSIM. By minimizing such an empirical version, we estimate the homogeneous parameter and the subgroup-averages of the heterogeneous index directions, and then use a fusion penalized method to identify the subgroup structure of the PHSIM. By the proposed methodologies, the homogeneous parameter and the heterogeneous index directions can be consistently estimated, and the heterogeneous parameters can be consistently clustered. Moreover, the new clustering procedure is simple and robust. Simulation studies are carried out to examine the performance of the proposed methodologies.

Keywords: Single index model; Homogeneity; Convex clustering; Subgroup-average; Estimation consistency (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s00362-020-01203-2

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