论文标题
估计扭结阈值和测试连续性时的最小风险
Minimax Risk in Estimating Kink Threshold and Testing Continuity
论文作者
论文摘要
在估计阈值参数的情况下，我们在不知道阈值回归模型是否连续的情况下得出了风险下限。随着样本量$ n $仅以立方根速率生长，界限为零。在这一发现的激励下，我们开发了针对阈值回归模型的连续性测试，并为计算其\ textit {p}值的引导程序。建立了引导程序的有效性，并通过蒙特卡洛模拟探索其有限样品特性。
We 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.
