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Pure Mathematics 2023
测量误差模型方差多变点的估计及收敛速度
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Abstract:
当已知测量误差模型中误差的方差存在变点时，对方差变点用特征函数构造了一个含有调节参数的“CUSUM型估计量”，研究了方差变点估计量的弱(强)相合性以及收敛速度，并结合“二元分割法”推广至多个方差变点的估计。利用基于数据驱动的调节参数选取方法选取适合的调节参数，并应用含有调节参数的“CUSUM型估计量”对黄金价格的涨跌幅的方差进行实证分析，结果表明基于调节参数“CUSUM型估计量”得到的方差变点与实际相符，且估计量更稳健。
When the variance of the measurement error model is known to have change points, a “CUSUM type estimator” with tuning parameters is constructed by using a characteristic function for each change point. The weak (strong) consistency and convergence rate of the variance change point estimation are studied, and the “binary segmentation method” is extended to estimate multiple variance change points. The data-driven tuning parameter selection method is used to select suitable tuning parameters, and using the “CUSUM type estimate” with tuning parameters to make an empirical analysis of the variance of the rise and fall of gold prices. The results show that the variance change points obtained based on the tuning parameter “CUSUM type estimator” are consistent with the reality, and the estimators are more robust.
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