{"title":"Optimal split-plot designs under individual word length patterns","authors":"Xiaoxue Han , Chong Sheng , Min-Qian Liu","doi":"10.1016/j.spl.2024.110311","DOIUrl":"10.1016/j.spl.2024.110311","url":null,"abstract":"<div><div>For multi-factor experiments that cannot run all the factors in a completely random order, fractional factorial split-plot (FFSP) designs are often used in practice. When some prior knowledge has shown that some factors are more likely to be significant than others, Han et al. (2023) proposed the individual word length patterns (IWLPs) of whole-plot (WP) and sub-plot (SP), denoted by the I<span><math><msub><mrow></mrow><mrow><mi>w</mi></mrow></msub></math></span>WLP and I<span><math><msub><mrow></mrow><mrow><mi>s</mi></mrow></msub></math></span>WLP respectively, in the FFSP design. In this paper, we propose a construction method for optimal FFSP designs based on these two criteria, where the key of the method is to construct generating matrices for different FFSP designs from the generating matrix of a fractional factorial design, and hence we get a class of effective FFSP designs. These designs are more applicable in many situations. The results for 16-run two-level FFSP designs are tabulated in the supplementary material for possible use by practitioners.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110311"},"PeriodicalIF":0.9,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143162107","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":"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":"Improving the Bickel–Rosenblatt global measure of deviation and goodness-of-fit test","authors":"S. Ejaz Ahmed , Mohamed Amezziane , Keshab Dahal","doi":"10.1016/j.spl.2024.110310","DOIUrl":"10.1016/j.spl.2024.110310","url":null,"abstract":"<div><div>We propose a zero-centered version of the Bickel–Rosenblatt statistic and use it to construct goodness of fit tests. We derive the null distributions and power functions of these tests along with their consistency results. A simulation study is carried out to show how the new tests outperform traditional ones.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"218 ","pages":"Article 110310"},"PeriodicalIF":0.9,"publicationDate":"2024-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143149200","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}
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