Minimax Risk in Estimating Kink Threshold and Testing Continuity

• Tác giả: Javier Hidalgo, Heejun Lee, Jungyoon Lee, Myung Hwan Seo
• Ngôn ngữ: eng
• Ký hiệu phân loại: 511.4 Approximations formerly also 513.24 and expansions
• Thông tin xuất bản: 2022
• Bộ sưu tập: Metadata
• ID: 194565

Tóm tắt

Comment: arXiv admin note: text overlap with arXiv:1702.00836We derive a risk lower bound in estimating the threshold parameter without knowing whether the threshold regression model is continuous or not. The bound goes to zero as the sample size $ n $ grows only at the cube root rate. Motivated by this finding, we develop a continuity test for the threshold regression model and a bootstrap to compute its \textit{p}-values. The validity of the bootstrap is established, and its finite sample property is explored through Monte Carlo simulations.