This paper discusses a test of goodness-of-fit of a known error density in a two phase linear regression model in the case jump size at the phase transition point is fixed or tends to zero with the increasing sample size. The proposed test is based on an integrated square difference between a nonparametric error density estimator obtained from the residuals and its expected value under the null error density when the underlying regression parameters are known. The paper establishes the asymptotic normality of the proposed test statistic under the null hypothesis and under certain global \(L_2\) alternatives. The asymptotic null distribution of the test statistic is the same as in the case of the known regression parameters. Under the chosen alternatives, unlike in the linear autoregressive time series models with known intercept, it depends on the parameters and their estimates in general. We also describe the analogous results for the self-exciting threshold autoregressive time series model of order 1.

本文讨论了在相变点处的跳跃大小固定或随着样本量的增加趋于零的情况下，两相线性回归模型中已知误差密度的拟合优度检验。当基础回归参数已知时，所提出的测试基于从残差获得的非参数误差密度估计与其在零误差密度下的预期值之间的积分平方差。本文建立了在原假设和特定全局\(L_2\)下所提出的检验统计量的渐近正态性。备择方案。检验统计量的渐近零分布与已知回归参数的情况相同。在所选择的备选方案下，与已知截距的线性自回归时间序列模型不同，它通常取决于参数及其估计值。我们还描述了 1 阶自激阈值自回归时间序列模型的类似结果。