Pub Date : 2024-11-14DOI: 10.1016/j.spl.2024.110306
Jianan Shi , Zhenhong Yu , Yu Miao
Let be a sequence of independent and identically distributed non-negative random variables with heavy tails and be an array of non-negative numbers. In the present paper, we study the large deviation of infinite weighted sums , which is a supplement of Aurzada (2020).
{"title":"A supplement to the large deviations of infinite weighted sums of heavy tailed random variables","authors":"Jianan Shi , Zhenhong Yu , Yu Miao","doi":"10.1016/j.spl.2024.110306","DOIUrl":"10.1016/j.spl.2024.110306","url":null,"abstract":"<div><div>Let <span><math><mrow><mo>{</mo><mi>X</mi><mo>,</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>,</mo><mi>n</mi><mo>≥</mo><mn>1</mn><mo>}</mo></mrow></math></span> be a sequence of independent and identically distributed non-negative random variables with heavy tails and <span><math><mrow><mo>{</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>i</mi></mrow></msub><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow><mo>,</mo><mi>i</mi><mo>≥</mo><mn>1</mn><mo>,</mo><mi>n</mi><mo>≥</mo><mn>1</mn><mo>}</mo></mrow></math></span> be an array of non-negative numbers. In the present paper, we study the large deviation of infinite weighted sums <span><math><mrow><msubsup><mrow><mo>∑</mo></mrow><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>∞</mi></mrow></msubsup><msub><mrow><mi>a</mi></mrow><mrow><mi>i</mi></mrow></msub><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow><msub><mrow><mi>X</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></math></span>, which is a supplement of Aurzada (2020).</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"217 ","pages":"Article 110306"},"PeriodicalIF":0.9,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142663764","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}
Pub Date : 2024-11-12DOI: 10.1016/j.spl.2024.110304
J.A. Christen , F.J. Rubio
We propose a parametric hazard model obtained by enforcing positivity in the damped harmonic oscillator. The resulting model has closed-form hazard and cumulative hazard functions, facilitating likelihood and Bayesian inference on the parameters. We show that this model can capture a range of hazard shapes, such as increasing, decreasing, unimodal, bathtub, and oscillatory patterns, and characterize the tails of the corresponding survival function. We illustrate the use of this model in survival analysis using real data.
{"title":"On harmonic oscillator hazard functions","authors":"J.A. Christen , F.J. Rubio","doi":"10.1016/j.spl.2024.110304","DOIUrl":"10.1016/j.spl.2024.110304","url":null,"abstract":"<div><div>We propose a parametric hazard model obtained by enforcing positivity in the damped harmonic oscillator. The resulting model has closed-form hazard and cumulative hazard functions, facilitating likelihood and Bayesian inference on the parameters. We show that this model can capture a range of hazard shapes, such as increasing, decreasing, unimodal, bathtub, and oscillatory patterns, and characterize the tails of the corresponding survival function. We illustrate the use of this model in survival analysis using real data.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"217 ","pages":"Article 110304"},"PeriodicalIF":0.9,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142663816","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}
Pub Date : 2024-11-06DOI: 10.1016/j.spl.2024.110305
Timofei Shashkov
<div><div>Let <span><math><mrow><mi>B</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mrow><mo>(</mo><msub><mrow><mi>B</mi></mrow><mrow><mn>1</mn></mrow></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><msub><mrow><mi>B</mi></mrow><mrow><mn>2</mn></mrow></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow></math></span>, <span><math><mrow><mi>t</mi><mo>≥</mo><mn>0</mn></mrow></math></span> be a two-dimensional Brownian motion with independent components and define the <span><math><mi>γ</mi></math></span>-reflected process <span><span><span><math><mrow><mi>X</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mrow><mo>(</mo><msub><mrow><mi>X</mi></mrow><mrow><mn>1</mn></mrow></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><msub><mrow><mi>X</mi></mrow><mrow><mn>2</mn></mrow></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>)</mo></mrow><mo>=</mo><mfenced><mrow><msub><mrow><mi>B</mi></mrow><mrow><mn>1</mn></mrow></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>−</mo><msub><mrow><mi>c</mi></mrow><mrow><mn>1</mn></mrow></msub><mi>t</mi><mo>−</mo><msub><mrow><mi>γ</mi></mrow><mrow><mn>1</mn></mrow></msub><munder><mrow><mo>inf</mo></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>∈</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>t</mi><mo>]</mo></mrow></mrow></munder><mrow><mo>(</mo><msub><mrow><mi>B</mi></mrow><mrow><mn>1</mn></mrow></msub><mrow><mo>(</mo><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo></mrow><mo>−</mo><msub><mrow><mi>c</mi></mrow><mrow><mn>1</mn></mrow></msub><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo></mrow><mo>,</mo><msub><mrow><mi>B</mi></mrow><mrow><mn>2</mn></mrow></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>−</mo><msub><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msub><mi>t</mi><mo>−</mo><msub><mrow><mi>γ</mi></mrow><mrow><mn>2</mn></mrow></msub><munder><mrow><mo>inf</mo></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>∈</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>t</mi><mo>]</mo></mrow></mrow></munder><mrow><mo>(</mo><msub><mrow><mi>B</mi></mrow><mrow><mn>2</mn></mrow></msub><mrow><mo>(</mo><msub><mrow><mi>s</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></mrow><mo>−</mo><msub><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mi>s</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></mrow></mrow></mfenced><mo>,</mo></mrow></math></span></span></span>with given finite constants <span><math><mrow><msub><mrow><mi>c</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>∈</mo><mi>R</mi></mrow></math></span> and <span><math><mrow><msub><mrow><mi>γ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>γ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>∈</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></mrow></math></span>. The goal of this paper is to deri
{"title":"Ruin probability approximation for bidimensional Brownian risk model with tax","authors":"Timofei Shashkov","doi":"10.1016/j.spl.2024.110305","DOIUrl":"10.1016/j.spl.2024.110305","url":null,"abstract":"<div><div>Let <span><math><mrow><mi>B</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mrow><mo>(</mo><msub><mrow><mi>B</mi></mrow><mrow><mn>1</mn></mrow></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><msub><mrow><mi>B</mi></mrow><mrow><mn>2</mn></mrow></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow></math></span>, <span><math><mrow><mi>t</mi><mo>≥</mo><mn>0</mn></mrow></math></span> be a two-dimensional Brownian motion with independent components and define the <span><math><mi>γ</mi></math></span>-reflected process <span><span><span><math><mrow><mi>X</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mrow><mo>(</mo><msub><mrow><mi>X</mi></mrow><mrow><mn>1</mn></mrow></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><msub><mrow><mi>X</mi></mrow><mrow><mn>2</mn></mrow></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>)</mo></mrow><mo>=</mo><mfenced><mrow><msub><mrow><mi>B</mi></mrow><mrow><mn>1</mn></mrow></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>−</mo><msub><mrow><mi>c</mi></mrow><mrow><mn>1</mn></mrow></msub><mi>t</mi><mo>−</mo><msub><mrow><mi>γ</mi></mrow><mrow><mn>1</mn></mrow></msub><munder><mrow><mo>inf</mo></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>∈</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>t</mi><mo>]</mo></mrow></mrow></munder><mrow><mo>(</mo><msub><mrow><mi>B</mi></mrow><mrow><mn>1</mn></mrow></msub><mrow><mo>(</mo><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo></mrow><mo>−</mo><msub><mrow><mi>c</mi></mrow><mrow><mn>1</mn></mrow></msub><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo></mrow><mo>,</mo><msub><mrow><mi>B</mi></mrow><mrow><mn>2</mn></mrow></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>−</mo><msub><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msub><mi>t</mi><mo>−</mo><msub><mrow><mi>γ</mi></mrow><mrow><mn>2</mn></mrow></msub><munder><mrow><mo>inf</mo></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>∈</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>t</mi><mo>]</mo></mrow></mrow></munder><mrow><mo>(</mo><msub><mrow><mi>B</mi></mrow><mrow><mn>2</mn></mrow></msub><mrow><mo>(</mo><msub><mrow><mi>s</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></mrow><mo>−</mo><msub><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mi>s</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></mrow></mrow></mfenced><mo>,</mo></mrow></math></span></span></span>with given finite constants <span><math><mrow><msub><mrow><mi>c</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>∈</mo><mi>R</mi></mrow></math></span> and <span><math><mrow><msub><mrow><mi>γ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>γ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>∈</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></mrow></math></span>. The goal of this paper is to deri","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"217 ","pages":"Article 110305"},"PeriodicalIF":0.9,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142663763","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}
Pub Date : 2024-11-04DOI: 10.1016/j.spl.2024.110292
Lijian Yang
Strict monotonicity is proved for the distributions of extremes of processes consisting of series of bounded function with independent random coefficients, in particular for zero mean continuous Gaussian processes over compact metric space. These results have wide applications to global inference problems on unknown functions.
{"title":"Strict monotonicity of stochastic process extreme distributions","authors":"Lijian Yang","doi":"10.1016/j.spl.2024.110292","DOIUrl":"10.1016/j.spl.2024.110292","url":null,"abstract":"<div><div>Strict monotonicity is proved for the distributions of extremes of processes consisting of series of bounded function with independent random coefficients, in particular for zero mean continuous Gaussian processes over compact metric space. These results have wide applications to global inference problems on unknown functions.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"217 ","pages":"Article 110292"},"PeriodicalIF":0.9,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142663815","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}
Pub Date : 2024-11-02DOI: 10.1016/j.spl.2024.110294
Keyi Mou, Zhiming Li, Jinlong Cheng
Observations are frequently generated in clinical trials from correlated multiple organs (or parts) of individuals. The statistical inference is little about conducting regression analysis based on such data. This paper first develops a logistic regression for correlated multiple responses using a stable correlation binomial (SCB) model. Then, we obtain maximum likelihood estimators (MLEs) of unknown parameters through a fast quadratic lower bound (QLB) algorithm. Further, likelihood ratio, score and Wald statistics are used to test the effect of covariates based on the MLEs. Finally, the QLB algorithm and asymptotic tests are evaluated through simulations and applied to real dental data.
{"title":"Parameter estimation and hypothesis tests in logistic model for complex correlated data","authors":"Keyi Mou, Zhiming Li, Jinlong Cheng","doi":"10.1016/j.spl.2024.110294","DOIUrl":"10.1016/j.spl.2024.110294","url":null,"abstract":"<div><div>Observations are frequently generated in clinical trials from correlated multiple organs (or parts) of individuals. The statistical inference is little about conducting regression analysis based on such data. This paper first develops a logistic regression for correlated multiple responses using a stable correlation binomial (SCB) model. Then, we obtain maximum likelihood estimators (MLEs) of unknown parameters through a fast quadratic lower bound (QLB) algorithm. Further, likelihood ratio, score and Wald statistics are used to test the effect of covariates based on the MLEs. Finally, the QLB algorithm and asymptotic tests are evaluated through simulations and applied to real dental data.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"217 ","pages":"Article 110294"},"PeriodicalIF":0.9,"publicationDate":"2024-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142594046","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}
Pub Date : 2024-10-30DOI: 10.1016/j.spl.2024.110288
Tommy Wright
Klein, Wright, and Wieczorek (2020), hereafter KWW, constructs a simple novel measure of uncertainty for an estimated ranking using a joint confidence region for the true ranking of populations. In this current paper, our proposed framework permits some control over the amount of uncertainty and tightness in various portions of the estimated ranking with an optimal allocation of sample among the populations.
Klein、Wright 和 Wieczorek（2020 年）（以下简称 KWW）利用 K 种群真实排名的联合置信区域，为估计排名构建了一个简单的新型不确定性度量。在本文中，我们提出的框架允许通过在 K 个种群中优化样本分配，对估计排名各部分的不确定性和严密性进行一定程度的控制。
{"title":"Optimal tightening of the KWW joint confidence region for a ranking","authors":"Tommy Wright","doi":"10.1016/j.spl.2024.110288","DOIUrl":"10.1016/j.spl.2024.110288","url":null,"abstract":"<div><div>Klein, Wright, and Wieczorek (2020), hereafter KWW, constructs a simple novel measure of uncertainty for an estimated ranking using a joint confidence region for the true ranking of <span><math><mi>K</mi></math></span> populations. In this current paper, our proposed framework permits some control over the amount of uncertainty and tightness in various portions of the estimated ranking with an optimal allocation of sample among the <span><math><mi>K</mi></math></span> populations.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"217 ","pages":"Article 110288"},"PeriodicalIF":0.9,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142651260","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}
Pub Date : 2024-10-29DOI: 10.1016/j.spl.2024.110293
Minyuan Lu, Bu Zhou
This study focuses on the high-dimensional one-way analysis of variance problem, specifically, testing whether multiple population mean vectors are equal in the context of high-dimensional data. To solve the problem that classical multivariate analysis of variance (MANOVA) test statistics are undefined when the dimensionality surpasses the sample size, we propose a random permutation test using low-dimensional subspaces obtained by clustering of variables. The test statistics are derived from a one-way MANOVA decomposition for clustered variables and this approach utilizes the correlation information among variables to ensure high testing power. Simulation studies indicate that the proposed test performs well with high-dimensional data.
{"title":"A one-way MANOVA test for high-dimensional data using clustering subspaces","authors":"Minyuan Lu, Bu Zhou","doi":"10.1016/j.spl.2024.110293","DOIUrl":"10.1016/j.spl.2024.110293","url":null,"abstract":"<div><div>This study focuses on the high-dimensional one-way analysis of variance problem, specifically, testing whether multiple population mean vectors are equal in the context of high-dimensional data. To solve the problem that classical multivariate analysis of variance (MANOVA) test statistics are undefined when the dimensionality surpasses the sample size, we propose a random permutation test using low-dimensional subspaces obtained by clustering of variables. The test statistics are derived from a one-way MANOVA decomposition for clustered variables and this approach utilizes the correlation information among variables to ensure high testing power. Simulation studies indicate that the proposed test performs well with high-dimensional data.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"217 ","pages":"Article 110293"},"PeriodicalIF":0.9,"publicationDate":"2024-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142594045","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}
Pub Date : 2024-10-28DOI: 10.1016/j.spl.2024.110290
Chi Zhang, Danna Zhang
Probability and moment inequalities for quadratic forms are valuable tools in studying the properties of second-order statistics. There are extensive results regarding quadratic forms in random variables with finite exponential moments. However, the counterpart that allows for weaker moment conditions is inadequate. In this work, we present a new Nagaev-type tail probability inequality and a Rosenthal-type moment inequality for quadratic forms in random variables with fat tails.
{"title":"Probability and moment inequalities for quadratic forms in independent random variables with fat tails","authors":"Chi Zhang, Danna Zhang","doi":"10.1016/j.spl.2024.110290","DOIUrl":"10.1016/j.spl.2024.110290","url":null,"abstract":"<div><div>Probability and moment inequalities for quadratic forms are valuable tools in studying the properties of second-order statistics. There are extensive results regarding quadratic forms in random variables with finite exponential moments. However, the counterpart that allows for weaker moment conditions is inadequate. In this work, we present a new Nagaev-type tail probability inequality and a Rosenthal-type moment inequality for quadratic forms in random variables with fat tails.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"217 ","pages":"Article 110290"},"PeriodicalIF":0.9,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142572986","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}
Pub Date : 2024-10-26DOI: 10.1016/j.spl.2024.110289
Issey Sukeda , Tomonari Sei
In this work, we demonstrate that the Frank copula is the minimum information copula under fixed Kendall’s (MICK), both theoretically and numerically. First, we explain that both MICK and the Frank density follow the hyperbolic Liouville equation. Subsequently, we show that the copula density satisfying the Liouville equation is uniquely the Frank copula. Our result asserts that selecting the Frank copula as an appropriate copula model is equivalent to using Kendall’s as the sole available information about the true distribution, based on the entropy maximization principle.
在这项工作中，我们从理论和数值两方面证明了弗兰克协整是固定肯德尔τ（MICK）条件下的最小信息协整。首先，我们解释了 MICK 和 Frank 密度都遵循双曲 Liouville 方程。随后，我们证明满足 Liouville 方程的 copula 密度是唯一的 Frank copula。我们的结果证明，根据熵最大化原则，选择 Frank copula 作为合适的 copula 模型等同于使用 Kendall's τ 作为关于真实分布的唯一可用信息。
{"title":"Frank copula is minimum information copula under fixed Kendall’s τ","authors":"Issey Sukeda , Tomonari Sei","doi":"10.1016/j.spl.2024.110289","DOIUrl":"10.1016/j.spl.2024.110289","url":null,"abstract":"<div><div>In this work, we demonstrate that the Frank copula is the minimum information copula under fixed Kendall’s <span><math><mi>τ</mi></math></span> (MICK), both theoretically and numerically. First, we explain that both MICK and the Frank density follow the hyperbolic Liouville equation. Subsequently, we show that the copula density satisfying the Liouville equation is uniquely the Frank copula. Our result asserts that selecting the Frank copula as an appropriate copula model is equivalent to using Kendall’s <span><math><mi>τ</mi></math></span> as the sole available information about the true distribution, based on the entropy maximization principle.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"217 ","pages":"Article 110289"},"PeriodicalIF":0.9,"publicationDate":"2024-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142551915","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}
Pub Date : 2024-10-24DOI: 10.1016/j.spl.2024.110287
Ying Huang, Jun Peng
We consider a robust optimal investment and reinsurance problem with multiple dependent risks for an Ambiguity-Averse Insurer (AAI), who wishes to minimize the probability that the value of the wealth process reaches a low barrier before a high goal. We assume that the insurer can purchase per-loss reinsurance for every class of insurance business and invest its surplus in a risk-free asset and a risky asset. Using the technique of stochastic control theory and solving the associated Hamilton-Jacobi-Bellman (HJB) equation, we derive the robust optimal investment-reinsurance strategy and the associated value function. We conclude that the robust optimal investment-reinsurance strategy coincides with the one without model ambiguity, but the value function differs. We also illustrate our results by numerical examples.
{"title":"Minimizing the penalized goal-reaching probability with multiple dependent risks","authors":"Ying Huang, Jun Peng","doi":"10.1016/j.spl.2024.110287","DOIUrl":"10.1016/j.spl.2024.110287","url":null,"abstract":"<div><div>We consider a robust optimal investment and reinsurance problem with multiple dependent risks for an Ambiguity-Averse Insurer (AAI), who wishes to minimize the probability that the value of the wealth process reaches a low barrier before a high goal. We assume that the insurer can purchase per-loss reinsurance for every class of insurance business and invest its surplus in a risk-free asset and a risky asset. Using the technique of stochastic control theory and solving the associated Hamilton-Jacobi-Bellman (HJB) equation, we derive the robust optimal investment-reinsurance strategy and the associated value function. We conclude that the robust optimal investment-reinsurance strategy coincides with the one without model ambiguity, but the value function differs. We also illustrate our results by numerical examples.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"217 ","pages":"Article 110287"},"PeriodicalIF":0.9,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142572987","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}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号