Least squares estimation of a quasiconvex regression function

• 成果类型: Article
• 署名作者: Mukherjee, Somabha; Patra, Rohit K.; Johnson, Andrew L.; Morita, Hiroshi
• 署名单位: National University of Singapore; State University System of Florida; University of Florida; Texas A&M University System; Texas A&M University College Station; University of Osaka
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1093/jrsssb/qkad133
• 发表日期: 2024
• 页码: 512-534
• 关键词: isotonic regression; Oracle Inequalities; risk bounds; algorithm; selection

摘要

We develop a new approach for the estimation of a multivariate function based on the economic axioms of quasiconvexity (and monotonicity). On the computational side, we prove the existence of the quasiconvex constrained least squares estimator (LSE) and provide a characterisation of the function space to compute the LSE via a mixed-integer quadratic programme. On the theoretical side, we provide finite sample risk bounds for the LSE via a sharp oracle inequality. Our results allow for errors to depend on the covariates and to have only two finite moments. We illustrate the superior performance of the LSE against some competing estimators via simulation. Finally, we use the LSE to estimate the production function for the Japanese plywood industry and the cost function for hospitals across the US.