{"title":"Asymptotics for the conditional self-weighted \n \n \n M\n \n $$ M $$\n estimator of GRCA(\n \n \n p\n \n $$ p $$\n ) models and its statistical inference","authors":"Chi Yao, Wei Yu, Xuejun Wang","doi":"10.1111/anzs.12408","DOIUrl":null,"url":null,"abstract":"<div>\n \n <p>Under the <math>\n <semantics>\n <mrow>\n <mi>p</mi>\n </mrow>\n <annotation>$$ p $$</annotation>\n </semantics></math>-order generalised random coefficient autoregressive (GRCA(<math>\n <semantics>\n <mrow>\n <mi>p</mi>\n </mrow>\n <annotation>$$ p $$</annotation>\n </semantics></math>)) model with random coefficients <math>\n <semantics>\n <mrow>\n <msub>\n <mrow>\n <mi>Φ</mi>\n </mrow>\n <mrow>\n <mi>t</mi>\n </mrow>\n </msub>\n <mo>,</mo>\n </mrow>\n <annotation>$$ {\\boldsymbol{\\Phi}}_t, $$</annotation>\n </semantics></math> we propose a conditional self-weighted <math>\n <semantics>\n <mrow>\n <mi>M</mi>\n </mrow>\n <annotation>$$ M $$</annotation>\n </semantics></math> estimator of <math>\n <semantics>\n <mrow>\n <mi>E</mi>\n <msub>\n <mrow>\n <mi>Φ</mi>\n </mrow>\n <mrow>\n <mi>t</mi>\n </mrow>\n </msub>\n </mrow>\n <annotation>$$ \\mathrm{E}{\\boldsymbol{\\Phi}}_t $$</annotation>\n </semantics></math>. 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.</p>\n </div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1111/anzs.12408","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Under the -order generalised random coefficient autoregressive (GRCA()) model with random coefficients we propose a conditional self-weighted estimator of . 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.