Statistics & Probability Letters最新文献

{"title":"Bayes minimax estimator of the mean vector in an elliptically contoured distribution","authors":"Jie Jiang ,&nbsp;Lichun Wang","doi":"10.1016/j.spl.2024.110186","DOIUrl":"https://doi.org/10.1016/j.spl.2024.110186","url":null,"abstract":"<div><p>This paper investigates the Bayes estimator of the mean of an elliptically contoured distribution with unknown scale parameter under the quadratic loss. The Laplace transform and inverse Laplace transform of density facilitate us to obtain the expression of Bayes estimator. Then we prove the minimaxity of the Bayes estimator under certain conditions.</p></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141484822","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":"Instrument-residual estimator for multi-valued instruments under full monotonicity","authors":"Bora Kim ,&nbsp;Myoung-jae Lee","doi":"10.1016/j.spl.2024.110187","DOIUrl":"https://doi.org/10.1016/j.spl.2024.110187","url":null,"abstract":"<div><p>In determining the effects of a binary treatment <span><math><mi>D</mi></math></span> on an outcome <span><math><mi>Y</mi></math></span>, a multi-valued instrumental variable (IV) <span><math><mrow><mi>Z</mi><mo>=</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>J</mi></mrow></math></span> often appears. <span>Imbens and Angrist (1994, Econometrica)</span> showed that the IV estimator (IVE) of <span><math><mi>Y</mi></math></span> on <span><math><mi>D</mi></math></span> using <span><math><mi>Z</mi></math></span> as an IV is consistent for a non-negatively weighted average of heterogeneous “complier” effects. However, Imbens and Angrist did not include covariates <span><math><mi>X</mi></math></span>. This paper generalizes their finding by explicitly allowing <span><math><mi>X</mi></math></span> to appear in the linear model for the IVE, and shows that the extra condition <span><math><mrow><mi>E</mi><mrow><mo>(</mo><mi>Z</mi><mo>|</mo><mi>X</mi><mo>)</mo></mrow><mo>=</mo><mi>L</mi><mrow><mo>(</mo><mi>Z</mi><mo>|</mo><mi>X</mi><mo>)</mo></mrow></mrow></math></span> is necessary for generalization, where <span><math><mrow><mi>L</mi><mrow><mo>(</mo><mi>Z</mi><mo>|</mo><mi>X</mi><mo>)</mo></mrow><mo>≡</mo><mi>E</mi><mrow><mo>(</mo><mi>Z</mi><msup><mrow><mi>X</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>)</mo></mrow><msup><mrow><mrow><mo>{</mo><mi>E</mi><mrow><mo>(</mo><mi>X</mi><msup><mrow><mi>X</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>)</mo></mrow><mo>}</mo></mrow></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mi>X</mi></mrow></math></span> is the linear projection. This paper therefore proposes an alternative IVE using <span><math><mrow><mi>Z</mi><mo>−</mo><mi>E</mi><mrow><mo>(</mo><mi>Z</mi><mo>|</mo><mi>X</mi><mo>)</mo></mrow></mrow></math></span> as an IV, which is consistent for the same estimand <em>without</em> the restrictive extra condition. A simulation study demonstrates that the extra condition <span><math><mrow><mi>E</mi><mrow><mo>(</mo><mi>Z</mi><mo>|</mo><mi>X</mi><mo>)</mo></mrow><mo>=</mo><mi>L</mi><mrow><mo>(</mo><mi>Z</mi><mo>|</mo><mi>X</mi><mo>)</mo></mrow></mrow></math></span> is necessary for the usual IVE, but not for the alternative IVE proposed in this paper.</p></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141481409","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":"Weighted Simplex Centroid Mixture Experiments for third order Becker’s models: The R-optimal approach","authors":"Bushra Husain ,&nbsp;Fariha Aslam","doi":"10.1016/j.spl.2024.110189","DOIUrl":"https://doi.org/10.1016/j.spl.2024.110189","url":null,"abstract":"<div><p>The R-optimality criterion, suggested as a substitute for the widely used D-optimality criteria, is employed in experimental designs when the primary goal is to create a rectangular confidence region. This study explores R-optimal designs concerning third order Becker’s models and calculates weights for values of <span><math><mrow><mn>3</mn><mo>≤</mo><mi>q</mi><mo>≤</mo><mn>10</mn></mrow></math></span>. Additionally, it compares and contrasts the D-optimal and R-optimal designs.</p></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141481412","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":"Frisch–Waugh–Lovell theorem-type results for the k-Class and 2SGMM estimators","authors":"Deepankar Basu","doi":"10.1016/j.spl.2024.110188","DOIUrl":"https://doi.org/10.1016/j.spl.2024.110188","url":null,"abstract":"<div><p>The Frisch–Waugh–Lovell (FWL) theorem shows that for the least squares estimator, parameter estimates from full and partial models are identically same. I show that in linear regression models with a mix of exogenous and endogenous regressors, FWL theorem-type results hold for the k-class estimators (including LIML) and the two-step optimal GMM estimator.</p></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141434830","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":"Simultaneous computation of Kendall’s tau and its jackknife variance","authors":"Samuel Perreault","doi":"10.1016/j.spl.2024.110181","DOIUrl":"https://doi.org/10.1016/j.spl.2024.110181","url":null,"abstract":"<div><p>We present efficient algorithms for simultaneously computing Kendall’s tau and the jackknife estimator of its variance. For the classical pairwise tau, we describe a modification of Knight’s algorithm (originally designed to compute only tau) that does so while preserving its <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mi>n</mi><msub><mrow><mo>log</mo></mrow><mrow><mn>2</mn></mrow></msub><mi>n</mi><mo>)</mo></mrow></mrow></math></span> runtime in the number of observations <span><math><mi>n</mi></math></span>. We also introduce a novel algorithm computing a multivariate extension of tau and its jackknife variance in <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mi>n</mi><msubsup><mrow><mo>log</mo></mrow><mrow><mn>2</mn></mrow><mrow><mi>p</mi></mrow></msubsup><mi>n</mi><mo>)</mo></mrow></mrow></math></span> time.</p></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167715224001500/pdfft?md5=5b3841ee52600a218d235751bb715c3c&pid=1-s2.0-S0167715224001500-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141481410","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":"Lower bounds for the trade-off between bias and mean absolute deviation","authors":"Alexis Derumigny ,&nbsp;Johannes Schmidt-Hieber","doi":"10.1016/j.spl.2024.110182","DOIUrl":"https://doi.org/10.1016/j.spl.2024.110182","url":null,"abstract":"<div><p>In nonparametric statistics, rate-optimal estimators typically balance bias and stochastic error. The recent work on overparametrization raises the question whether rate-optimal estimators exist that do not obey this trade-off. In this work we consider pointwise estimation in the Gaussian white noise model with regression function <span><math><mi>f</mi></math></span> in a class of <span><math><mi>β</mi></math></span>-Hölder smooth functions. Let ’worst-case’ refer to the supremum over all functions <span><math><mi>f</mi></math></span> in the Hölder class. It is shown that any estimator with worst-case bias <span><math><mrow><mo>≲</mo><msup><mrow><mi>n</mi></mrow><mrow><mo>−</mo><mi>β</mi><mo>/</mo><mrow><mo>(</mo><mn>2</mn><mi>β</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></mrow></msup><mo>≕</mo><msub><mrow><mi>ψ</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></math></span> must necessarily also have a worst-case mean absolute deviation that is lower bounded by <span><math><mrow><mo>≳</mo><msub><mrow><mi>ψ</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>.</mo></mrow></math></span> To derive the result, we establish abstract inequalities relating the change of expectation for two probability measures to the mean absolute deviation.</p></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167715224001512/pdfft?md5=51662c001093a4b55185099a04b71ff2&pid=1-s2.0-S0167715224001512-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141424191","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":"Weak approximation of Schrödinger–Föllmer diffusion","authors":"Koya Endo,&nbsp;Yumiharu Nakano","doi":"10.1016/j.spl.2024.110171","DOIUrl":"https://doi.org/10.1016/j.spl.2024.110171","url":null,"abstract":"<div><p>We consider the weak convergence of the Euler–Maruyama approximation for Schrödinger–Föllmer diffusions, which are solutions of Schrödinger bridge problems and can be used for sampling from given distributions. We show that the distribution of the terminal random variable of the time-discretized process weakly converges to the target one under mild regularity conditions.</p></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167715224001408/pdfft?md5=b5afb3ddb3bfc9440dc9d67d44f31603&pid=1-s2.0-S0167715224001408-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141314597","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":"On Yu and Hoff’s confidence intervals for treatment means","authors":"Paul Kabaila","doi":"10.1016/j.spl.2024.110170","DOIUrl":"https://doi.org/10.1016/j.spl.2024.110170","url":null,"abstract":"<div><p>Yu and Hoff constructed novel confidence intervals for the treatment means in a one-way layout. They assessed the expected lengths of these intervals using a semi-Bayesian analysis. We provide a revealing assessment of these expected lengths using a fully frequentist analysis.</p></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167715224001391/pdfft?md5=2d100e660e5414aefc69743d01f0c8c4&pid=1-s2.0-S0167715224001391-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141302933","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":"Short cycles of random permutations with cycle weights: Point processes approach","authors":"Oleksii Galganov ,&nbsp;Andrii Ilienko","doi":"10.1016/j.spl.2024.110169","DOIUrl":"https://doi.org/10.1016/j.spl.2024.110169","url":null,"abstract":"<div><p>We study the asymptotic behavior of short cycles of random permutations with cycle weights. More specifically, on a specially constructed metric space whose elements encode all possible cycles, we consider a point process containing all information on cycles of a given random permutation on <span><math><mrow><mo>{</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>n</mi><mo>}</mo></mrow></math></span>. The main result of the paper is the distributional convergence with respect to the vague topology of the above processes towards a Poisson point process as <span><math><mrow><mi>n</mi><mo>→</mo><mi>∞</mi></mrow></math></span> for a wide range of cycle weights. As an application, we give several limit theorems for various statistics of cycles.</p></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141302851","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 negative correlation of Arboreal Gas for specific parameters","authors":"Xiangyu Huang","doi":"10.1016/j.spl.2024.110174","DOIUrl":"https://doi.org/10.1016/j.spl.2024.110174","url":null,"abstract":"<div><p>Arboreal Gas is a type of (unrooted) random forest on a graph, where the probability is determined by a parameter <span><math><mrow><mi>β</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span> per edge. This model can be considered as the limit of the <span><math><mi>q</mi></math></span>-states random cluster model with <span><math><mrow><mi>p</mi><mo>=</mo><mi>β</mi><mi>q</mi></mrow></math></span> as <span><math><mrow><mi>q</mi><mo>→</mo><mn>0</mn></mrow></math></span>. A natural question arises regarding the existence and performance of the weak limit of Arboreal Gas as the graph size goes to infinity. The answer to this question relies on the negative correlation of Arboreal Gas, which is still an open problem. This paper primarily focuses on the negative correlation of Arboreal Gas and provides some results for specific parameters.</p></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141290682","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}