Asymptotics for the conditional self-weighted M $$ M $$ estimator of GRCA( p $$ p $$ ) models and its statistical inference

Pub Date : 2024-02-21 DOI:10.1111/anzs.12408

Chi Yao, Wei Yu, Xuejun Wang

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Abstract

Under the $p$ -order generalised random coefficient autoregressive (GRCA( $p$ )) model with random coefficients $Φ_{t},$ we propose a conditional self-weighted $M$ estimator of $E Φ_{t}$ . We investigate the asymptotic normality of this estimator with possibly heavy-tailed random variables. Furthermore, a Wald test statistic is constructed for the linear restriction on the parameters. In addition, the simulation experiments are carried out to assess the finite sample performance of theoretical results. Finally, a real data analysis about the increase (%) in the number of construction projects this year over the same period of last year is provided.

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GRCA(p$$ p$$) 模型的条件自加权 M$$ M$$ 估计器的渐近性及其统计推论

摘要在具有随机系数的-阶广义随机系数自回归（GRCA()）模型下，我们提出了一个条件自加权估计器。我们研究了该估计器在可能存在重尾随机变量的情况下的渐近正态性。此外，我们还构建了参数线性限制的 Wald 检验统计量。此外，我们还进行了模拟实验，以评估理论结果的有限样本性能。最后，提供了有关今年建筑项目数量比去年同期增长（%）的真实数据分析。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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