{"title":"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","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":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":55428,\"journal\":{\"name\":\"Australian & New Zealand Journal of Statistics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-02-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Australian & New Zealand Journal of Statistics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1111/anzs.12408\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Australian & New Zealand Journal of Statistics","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1111/anzs.12408","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
Asymptotics for the conditional self-weighted
M
$$ M $$
estimator of GRCA(
p
$$ p $$
) models and its statistical inference
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.
期刊介绍：
The Australian & New Zealand Journal of Statistics is an international journal managed jointly by the Statistical Society of Australia and the New Zealand Statistical Association. Its purpose is to report significant and novel contributions in statistics, ranging across articles on statistical theory, methodology, applications and computing. The journal has a particular focus on statistical techniques that can be readily applied to real-world problems, and on application papers with an Australasian emphasis. Outstanding articles submitted to the journal may be selected as Discussion Papers, to be read at a meeting of either the Statistical Society of Australia or the New Zealand Statistical Association.
The main body of the journal is divided into three sections.
The Theory and Methods Section publishes papers containing original contributions to the theory and methodology of statistics, econometrics and probability, and seeks papers motivated by a real problem and which demonstrate the proposed theory or methodology in that situation. There is a strong preference for papers motivated by, and illustrated with, real data.
The Applications Section publishes papers demonstrating applications of statistical techniques to problems faced by users of statistics in the sciences, government and industry. A particular focus is the application of newly developed statistical methodology to real data and the demonstration of better use of established statistical methodology in an area of application. It seeks to aid teachers of statistics by placing statistical methods in context.
The Statistical Computing Section publishes papers containing new algorithms, code snippets, or software descriptions (for open source software only) which enhance the field through the application of computing. Preference is given to papers featuring publically available code and/or data, and to those motivated by statistical methods for practical problems.
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