Annals of the Institute of Statistical Mathematics ( IF 1 ) Pub Date : 2021-10-18 , DOI: 10.1007/s10463-021-00812-4 Victor V. Konev 1 , Sergey E. Vorobeychikov 1
For parameters in a threshold autoregressive process, the paper proposes a sequential modification of the least squares estimates with a specific stopping rule for collecting the data for each parameter. In the case of normal residuals, these estimates are exactly normally distributed in a wide range of unknown parameters. On the base of these estimates, a fixed-size confidence ellipsoid covering true values of parameters with prescribed probability is constructed. In the i.i.d. case with unspecified error distributions, the sequential estimates are asymptotically normally distributed uniformly in parameters belonging to any compact set in the ergodicity parametric region. Small-sample behavior of the estimates is studied via simulation data.
中文翻译:
阈值自回归模型中参数的固定精度估计
对于阈值自回归过程中的参数,本文提出了对最小二乘估计的顺序修改,并使用特定的停止规则来收集每个参数的数据。在正态残差的情况下,这些估计值完全正态分布在广泛的未知参数中。在这些估计的基础上,构建了一个固定大小的置信椭球,它以规定的概率覆盖了参数的真实值。在具有未指定误差分布的 iid 情况下,序列估计在属于遍历参数区域中任何紧凑集的参数中渐近正态分布。通过模拟数据研究估计的小样本行为。