{"title":"Semi-supervised estimation of a single-index varying-coefficient model","authors":"Peng Lai, Zhou Wang, Yurong Zhang","doi":"10.1016/j.spl.2024.110312","DOIUrl":"10.1016/j.spl.2024.110312","url":null,"abstract":"<div><div>We introduce a single-index varying-coefficient model for the Framingham heart disease data and propose a semi-supervised estimation method that effectively utilizes unlabeled data. The method outperforms traditional approaches in accuracy, as validated by simulations and real examples.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"218 ","pages":"Article 110312"},"PeriodicalIF":0.9,"publicationDate":"2024-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142756828","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}
{"title":"Berry–Esseen expansion and Cramér-type large deviation for run and tumble particles on one dimension","authors":"Wenxuan Chen, Zhi Qu","doi":"10.1016/j.spl.2024.110308","DOIUrl":"10.1016/j.spl.2024.110308","url":null,"abstract":"<div><div>In this paper, we consider the run and tumble particles on one-dimensional lattice <span><math><mi>Z</mi></math></span>. We derive Berry–Esseen bound for the active particle. Moreover, we also obtain the Cramér-type large deviation when the particle evolves on the discrete time set <span><math><mi>N</mi></math></span>.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"218 ","pages":"Article 110308"},"PeriodicalIF":0.9,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142744390","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}
{"title":"Is the effective sample size always less than n? A spatial regression approach","authors":"Clemente Ferrer, Ronny Vallejos","doi":"10.1016/j.spl.2024.110309","DOIUrl":"10.1016/j.spl.2024.110309","url":null,"abstract":"<div><div>In this paper, within a spatial statistics framework, we present an upper bound for the effective sample size (ESS) as defined by Vallejos and Osorio (2014), addressing a research gap regarding the mathematical properties of the ESS. There are certain correlation structures for which the ESS exceeds <span><math><mi>n</mi></math></span>, which is inconsistent with the maximum possible sample size. Our approach identifies conditions on the correlation matrix of a spatial process that ensure that the equivalent number of independent and identically distributed observations within a spatial sample of size <span><math><mi>n</mi></math></span> does not exceed <span><math><mi>n</mi></math></span>. This property is desirable because it ensures the effectiveness of reduction measures.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"218 ","pages":"Article 110309"},"PeriodicalIF":0.9,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142744480","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}
{"title":"On exact Bayesian credible sets for discrete parameters","authors":"Chaegeun Song, Bing Li","doi":"10.1016/j.spl.2024.110295","DOIUrl":"10.1016/j.spl.2024.110295","url":null,"abstract":"<div><div>We introduce a generalized Bayesian credible set that can achieve any preassigned credible level, addressing a limitation of the current credible sets. This is achieved by exploiting a connection between the highest posterior density set and the Neyman–Pearson lemma.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"218 ","pages":"Article 110295"},"PeriodicalIF":0.9,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142703931","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}
{"title":"The heavy-tail behavior of the difference of two dependent random variables","authors":"Yiqing Chen","doi":"10.1016/j.spl.2024.110307","DOIUrl":"10.1016/j.spl.2024.110307","url":null,"abstract":"<div><div>Consider <span><math><mrow><mi>Z</mi><mo>=</mo><mi>X</mi><mo>−</mo><mi>Y</mi></mrow></math></span>, the difference of two nonnegative dependent random variables. We investigate how the difference <span><math><mi>Z</mi></math></span> inherits the heavy tail property of the minuend <span><math><mi>X</mi></math></span> and is altered by the subtrahend <span><math><mi>Y</mi></math></span>. In the case where <span><math><mi>X</mi></math></span> and <span><math><mi>Y</mi></math></span> are tail independent, we prove that if <span><math><mi>X</mi></math></span> has a long tail <span><math><mrow><msub><mrow><mover><mrow><mi>F</mi></mrow><mo>¯</mo></mover></mrow><mrow><mi>X</mi></mrow></msub><mo>=</mo><mn>1</mn><mo>−</mo><msub><mrow><mi>F</mi></mrow><mrow><mi>X</mi></mrow></msub></mrow></math></span>, the asymptotic behavior of <span><math><msub><mrow><mover><mrow><mi>F</mi></mrow><mo>¯</mo></mover></mrow><mrow><mi>X</mi></mrow></msub></math></span> is exactly inherited by <span><math><mi>Z</mi></math></span>, that is, <span><math><mrow><msub><mrow><mover><mrow><mi>F</mi></mrow><mo>¯</mo></mover></mrow><mrow><mi>Z</mi></mrow></msub><mo>∼</mo><msub><mrow><mover><mrow><mi>F</mi></mrow><mo>¯</mo></mover></mrow><mrow><mi>X</mi></mrow></msub></mrow></math></span>, regardless of the tail behavior of <span><math><mi>Y</mi></math></span>. However, this result may not hold when <span><math><mi>X</mi></math></span> and <span><math><mi>Y</mi></math></span> exhibit tail dependence. Within the framework of bivariate regular variation, we show that the limit of the ratio <span><math><mfrac><mrow><msub><mrow><mover><mrow><mi>F</mi></mrow><mo>¯</mo></mover></mrow><mrow><mi>Z</mi></mrow></msub></mrow><mrow><msub><mrow><mover><mrow><mi>F</mi></mrow><mo>¯</mo></mover></mrow><mrow><mi>X</mi></mrow></msub></mrow></mfrac></math></span> can range over the closed interval <span><math><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></math></span>.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"218 ","pages":"Article 110307"},"PeriodicalIF":0.9,"publicationDate":"2024-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142703930","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}
{"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}
{"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}
{"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}
{"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}
{"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}
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