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On higher-order moments of INGARCH processes 关于 INGARCH 过程的高阶矩
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2024-07-02 DOI: 10.1016/j.spl.2024.110198
Christian H. Weiß
{"title":"On higher-order moments of INGARCH processes","authors":"Christian H. Weiß","doi":"10.1016/j.spl.2024.110198","DOIUrl":"https://doi.org/10.1016/j.spl.2024.110198","url":null,"abstract":"<div><p>For important count distributions, such as (zero-inflated) Poisson and (negative-)binomial, the <span><math><mi>k</mi></math></span>th factorial moment is proportional to the <span><math><mi>k</mi></math></span>th power of the mean. This property is utilized to derive a general approach for computing higher-order moments of integer-valued generalized autoregressive conditional heteroscedasticity (INGARCH) processes. The proposed approach covers a wide range of existing model specifications, and its potential benefits are illustrated by an analysis of skewness and excess kurtosis in INGARCH processes.</p></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167715224001676/pdfft?md5=1a05e917c26685be8f2bdbd5ed320859&pid=1-s2.0-S0167715224001676-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141542314","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Higher-order derivative of local times for space–time anisotropic Gaussian random fields 时空各向异性高斯随机场局部时间的高阶导数
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2024-06-29 DOI: 10.1016/j.spl.2024.110197
Zhenlong Chen, Peng Xu
{"title":"Higher-order derivative of local times for space–time anisotropic Gaussian random fields","authors":"Zhenlong Chen,&nbsp;Peng Xu","doi":"10.1016/j.spl.2024.110197","DOIUrl":"https://doi.org/10.1016/j.spl.2024.110197","url":null,"abstract":"<div><p>Let <span><math><mrow><mi>X</mi><mo>=</mo><mrow><mo>{</mo><mi>X</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>}</mo></mrow></mrow></math></span> be a centered space–time anisotropic Gaussian random field values in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>. Under some general conditions, the existence and smoothness (in the sense of Meyer-Watanabe) of the higher-order derivative of the local times of <span><math><mrow><mi>X</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span> are studied. Moreover, we show that the derivatives of the local time of <span><math><mrow><mi>X</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span> is jointly continuous on <span><math><mrow><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>×</mo><msup><mrow><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></mrow><mrow><mi>N</mi></mrow></msup></mrow></math></span>. The existing results on local times of fractional Brownian motion and other Gaussian random fields are extended to higher-order derivative of local times of more general space–time anisotropic Gaussian random fields.</p></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141542313","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Large deviations for the Yule–Walker estimator of near critical autoregressive processes 近临界自回归过程的 Yule-Walker 估计器的大偏差
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2024-06-29 DOI: 10.1016/j.spl.2024.110196
Xiaochang Wang , Shui Feng , Yiping Guo , Bruno N. Rémillard
{"title":"Large deviations for the Yule–Walker estimator of near critical autoregressive processes","authors":"Xiaochang Wang ,&nbsp;Shui Feng ,&nbsp;Yiping Guo ,&nbsp;Bruno N. Rémillard","doi":"10.1016/j.spl.2024.110196","DOIUrl":"https://doi.org/10.1016/j.spl.2024.110196","url":null,"abstract":"<div><p>The large deviation principle is established for the Yule–Walker estimator of the near critical order one autoregressive process. The rate function is identified explicitly. Our result shows that, at the exponential scale, one cannot distinguish between near critical and the critical Yule–Walker estimators.</p></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167715224001652/pdfft?md5=8c91327797986f45c565d9a45f468be2&pid=1-s2.0-S0167715224001652-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141582477","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Exact partially conditional binomial analysis for multinomial data in 2 × 2 tables 对 2 × 2 表中的多项式数据进行部分条件二项式精确分析
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2024-06-28 DOI: 10.1016/j.spl.2024.110195
Dennis D. Boos , Shannon Ari , Roger L. Berger
{"title":"Exact partially conditional binomial analysis for multinomial data in 2 × 2 tables","authors":"Dennis D. Boos ,&nbsp;Shannon Ari ,&nbsp;Roger L. Berger","doi":"10.1016/j.spl.2024.110195","DOIUrl":"https://doi.org/10.1016/j.spl.2024.110195","url":null,"abstract":"<div><p>Starting with Barnard (1945, 1947), many papers have shown that exact unconditional tests outperform Fisher’s Exact Test in 2 × 2 tables with independent binomial data. Less has been published about unconditional tests with multinomial data. However, in many multinomial 2 × 2 analyses, a binomial-like comparison of proportions is of interest rather than inference in terms of odds ratios. Thus, this paper proposes using a partially conditional binomial analysis with data that are actually multinomially distributed. This partially conditional analysis, conditioning on the row totals and then using the unconditional binomial analysis, is more powerful than the fully conditional Fisher’s Exact Test, has good power comparable to the fully unconditional multinomial analysis, and provides exact confidence intervals for the difference of proportions. Also, the partially conditional binomial analysis requires considerably less computation than the fully unconditional analysis.</p></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141542312","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
From law of the iterated logarithm to Zolotarev distance for supercritical branching processes in random environment 从迭代对数定律到随机环境中超临界分支过程的佐洛塔列夫距离
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2024-06-27 DOI: 10.1016/j.spl.2024.110194
Yinna Ye
{"title":"From law of the iterated logarithm to Zolotarev distance for supercritical branching processes in random environment","authors":"Yinna Ye","doi":"10.1016/j.spl.2024.110194","DOIUrl":"https://doi.org/10.1016/j.spl.2024.110194","url":null,"abstract":"<div><p>Consider <span><math><msub><mrow><mrow><mo>(</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></mrow></mrow><mrow><mi>n</mi><mo>⩾</mo><mn>0</mn></mrow></msub></math></span> a supercritical branching process in an independent and identically distributed environment. Based on some recent development in martingale limit theory, we established law of the iterated logarithm, strong law of large numbers, invariance principle and optimal convergence rate in the central limit theorem under Zolotarev and Wasserstein distances of order <span><math><mrow><mi>p</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo>]</mo></mrow></mrow></math></span> for the process <span><math><msub><mrow><mrow><mo>(</mo><mo>log</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></mrow></mrow><mrow><mi>n</mi><mo>⩾</mo><mn>0</mn></mrow></msub></math></span>.</p></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141542311","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Ordering results between two multiple-outlier finite δ-mixtures 两个多重离群值有限δ混合物之间的排序结果
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2024-06-25 DOI: 10.1016/j.spl.2024.110193
Raju Bhakta , Suchandan Kayal , Narayanaswamy Balakrishnan
{"title":"Ordering results between two multiple-outlier finite δ-mixtures","authors":"Raju Bhakta ,&nbsp;Suchandan Kayal ,&nbsp;Narayanaswamy Balakrishnan","doi":"10.1016/j.spl.2024.110193","DOIUrl":"https://doi.org/10.1016/j.spl.2024.110193","url":null,"abstract":"<div><p>In this paper, we have obtained sufficient conditions for comparing two multiple-outlier (M-O) finite <span><math><mi>δ</mi></math></span>-mixtures based on the usual stochastic order and reversed hazard rate order. We have assumed a general parametric family of distributions for the subpopulations. Many distributions satisfying baseline-related conditions in the established results have also been provided as examples.</p></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141484821","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Study of discrete-time Hawkes process and its compensator 离散时霍克斯过程及其补偿器研究
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2024-06-25 DOI: 10.1016/j.spl.2024.110192
Utpal Jyoti Deba Sarma, Dharmaraja Selvamuthu
{"title":"Study of discrete-time Hawkes process and its compensator","authors":"Utpal Jyoti Deba Sarma,&nbsp;Dharmaraja Selvamuthu","doi":"10.1016/j.spl.2024.110192","DOIUrl":"https://doi.org/10.1016/j.spl.2024.110192","url":null,"abstract":"<div><p>The discrete-time Hawkes process (DTHP) is a sub-class of <span><math><mi>g</mi></math></span>-functions that serves as a discrete-time version of the continuous-time Hawkes process (CTHP). Like the CTHP, the DTHP also has the self-exciting property and its intensity depends on the entire history. In this paper, we study the asymptotic behavior of the DTHP and its compensator. We further analyze the moment generating function (MGF) of the DTHP and obtain some bounds and convergence results on the scaled logarithmic MGF of the DTHP.</p></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141486716","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The existence and smoothness of self-intersection local time for a class of Gaussian processes 一类高斯过程的自交局部时间的存在性和平稳性
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2024-06-25 DOI: 10.1016/j.spl.2024.110190
Lin Xie, Wenqing Ni, Shuicao Zheng, Guowei Lei
{"title":"The existence and smoothness of self-intersection local time for a class of Gaussian processes","authors":"Lin Xie,&nbsp;Wenqing Ni,&nbsp;Shuicao Zheng,&nbsp;Guowei Lei","doi":"10.1016/j.spl.2024.110190","DOIUrl":"https://doi.org/10.1016/j.spl.2024.110190","url":null,"abstract":"<div><p>In this paper sufficient conditions for the existence and smoothness of the self-intersection local time of a class of Gaussian processes are given in the sense of Meyer–Watanabe through <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> convergence and Wiener chaos expansion. Let <span><math><mi>X</mi></math></span> be a centered Gaussian process, whose canonical metric <span><math><mrow><mi>E</mi><mrow><mo>[</mo><mrow><mo>(</mo><mi>X</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>−</mo><mi>X</mi><msup><mrow><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow><mo>]</mo></mrow></mrow></math></span> is commensurate with <span><math><mrow><msup><mrow><mi>σ</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mrow><mo>|</mo><mi>t</mi><mo>−</mo><mi>s</mi><mo>|</mo></mrow><mo>)</mo></mrow></mrow></math></span>, where <span><math><mrow><mi>σ</mi><mrow><mo>(</mo><mi>⋅</mi><mo>)</mo></mrow></mrow></math></span> is continuous, increasing and concave. If <span><math><mrow><msubsup><mrow><mo>∫</mo></mrow><mrow><mn>0</mn></mrow><mrow><mi>T</mi></mrow></msubsup><mfrac><mrow><mn>1</mn></mrow><mrow><mi>σ</mi><mrow><mo>(</mo><mi>γ</mi><mo>)</mo></mrow></mrow></mfrac><mi>d</mi><mi>γ</mi><mo>&lt;</mo><mi>∞</mi></mrow></math></span>, then the self-intersection local time of the Gaussian process exists, and if <span><math><mrow><msubsup><mrow><mo>∫</mo></mrow><mrow><mn>0</mn></mrow><mrow><mi>T</mi></mrow></msubsup><msup><mrow><mrow><mo>(</mo><mi>σ</mi><mrow><mo>(</mo><mi>γ</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow><mrow><mo>−</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><mi>d</mi><mi>γ</mi><mo>&lt;</mo><mi>∞</mi></mrow></math></span>, the self-intersection local time of the Gaussian process is smooth in the sense of Meyer–Watanabe.</p></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141481411","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The logGARCH stochastic volatility model logGARCH 随机波动率模型
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2024-06-22 DOI: 10.1016/j.spl.2024.110185
Hafida Guerbyenne , Fayçal Hamdi , Malika Hamrat
{"title":"The logGARCH stochastic volatility model","authors":"Hafida Guerbyenne ,&nbsp;Fayçal Hamdi ,&nbsp;Malika Hamrat","doi":"10.1016/j.spl.2024.110185","DOIUrl":"https://doi.org/10.1016/j.spl.2024.110185","url":null,"abstract":"<div><p>This article introduces a new class of stochastic volatility models called <span><math><mrow><mo>log</mo><mi>G</mi><mi>A</mi><mi>R</mi><mi>C</mi><mi>H</mi></mrow></math></span> Stochastic Volatility models (<span><math><mrow><mo>log</mo><mi>G</mi><mi>A</mi><mi>R</mi><mi>C</mi><mi>H</mi></mrow></math></span>-<span><math><mrow><mi>S</mi><mi>V</mi></mrow></math></span>). We establish the strict stationarity and second-order stationarity properties of this model class. Additionally, we provide conditions for the existence of higher-order moments. To estimate the parameters of the proposed model, we utilize a sequential Monte Carlo method. Finally, we assess the performance of the suggested estimation method through a simulation study.</p></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141486717","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Representation of solutions to quadratic 2BSDEs with unbounded terminal values 具有无限制终值的二次方 2BSDEs 解的表示法
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2024-06-20 DOI: 10.1016/j.spl.2024.110191
Kon-Gun Kim, Mun-Chol Kim, Ho-Jin Hwang
{"title":"Representation of solutions to quadratic 2BSDEs with unbounded terminal values","authors":"Kon-Gun Kim,&nbsp;Mun-Chol Kim,&nbsp;Ho-Jin Hwang","doi":"10.1016/j.spl.2024.110191","DOIUrl":"https://doi.org/10.1016/j.spl.2024.110191","url":null,"abstract":"<div><p>Second order backward stochastic differential equations (2BSDEs, for short) are one of useful tools in solving stochastic control problems with model uncertainty. In this paper, we prove a representation formula for quadratic 2BSDEs with an unbounded terminal value under a convex assumption on the generator. Because of the unboundedness of the terminal value, we are unable to use some fine properties of BMO martingales, which are often employed in the literature to deal with bounded solutions to quadratic backward stochastic differential equations. Instead, we utilize the <span><math><mi>θ</mi></math></span>-technique. We also prove an existence result under an additional assumption that the terminal value is of uniformly continuous.</p></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141484824","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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