Pub Date : 2026-02-02DOI: 10.1016/j.spl.2026.110670
Jongmin Lee , Sungkyu Jung
We study general M-estimators of location on Riemannian manifolds, extending classical notions such as the Fréchet mean by replacing the squared loss with a broad class of loss functions. Under minimal regularity conditions on the loss function and the underlying probability distribution, we establish theoretical guarantees for the existence and uniqueness of the associated population M-functional and the corresponding sample M-estimators. In particular, we provide sufficient conditions under which the population minimizer set is nonempty and reduces to a singleton, and under which the corresponding sample M-estimator is likewise uniquely defined. Our results offer a general framework for robust location estimation in non-Euclidean geometric spaces and unify prior uniqueness results under a broad class of convex losses.
{"title":"General M-estimators of location on Riemannian manifolds: Existence and uniqueness","authors":"Jongmin Lee , Sungkyu Jung","doi":"10.1016/j.spl.2026.110670","DOIUrl":"10.1016/j.spl.2026.110670","url":null,"abstract":"<div><div>We study general M-estimators of location on Riemannian manifolds, extending classical notions such as the Fréchet mean by replacing the squared loss with a broad class of loss functions. Under minimal regularity conditions on the loss function and the underlying probability distribution, we establish theoretical guarantees for the existence and uniqueness of the associated population M-functional and the corresponding sample M-estimators. In particular, we provide sufficient conditions under which the population minimizer set is nonempty and reduces to a singleton, and under which the corresponding sample M-estimator is likewise uniquely defined. Our results offer a general framework for robust location estimation in non-Euclidean geometric spaces and unify prior uniqueness results under a broad class of convex losses.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"233 ","pages":"Article 110670"},"PeriodicalIF":0.7,"publicationDate":"2026-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146190567","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 : 2026-02-02DOI: 10.1016/j.spl.2026.110663
Abdulaziz Alenazi , Khaled Mehrez
In this paper, we introduce the Stieltjes transform order, defined via the composition of the Laplace transform of a random variable. First, we establish the monotonicity of the hazard rate associated with a transformed distribution of a random variable . As a consequence, we derive a sharp lower bound for the Stieltjes transform of in terms of its first two inverse moments. Secondly, we investigate the Stieltjes transform ratio order and provide its characterizations, both via properties of the hazard rate and through the monotonicity properties of higher-order Stieltjes transforms together with moment inequalities. We further establish explicit connections between the proposed orders and classical stochastic orders, including equivalence with the usual stochastic order and implication from the likelihood ratio order. These results enhance our understanding of stochastic orders and open new avenues for applications in reliability theory, economics, and applied probability.
{"title":"The Stieltjes transform order and related ratio order","authors":"Abdulaziz Alenazi , Khaled Mehrez","doi":"10.1016/j.spl.2026.110663","DOIUrl":"10.1016/j.spl.2026.110663","url":null,"abstract":"<div><div>In this paper, we introduce the Stieltjes transform order, defined via the composition of the Laplace transform of a random variable. First, we establish the monotonicity of the hazard rate associated with a transformed distribution of a random variable <span><math><mi>X</mi></math></span>. As a consequence, we derive a sharp lower bound for the Stieltjes transform of <span><math><mi>X</mi></math></span> in terms of its first two inverse moments. Secondly, we investigate the Stieltjes transform ratio order and provide its characterizations, both via properties of the hazard rate and through the monotonicity properties of higher-order Stieltjes transforms together with moment inequalities. We further establish explicit connections between the proposed orders and classical stochastic orders, including equivalence with the usual stochastic order and implication from the likelihood ratio order. These results enhance our understanding of stochastic orders and open new avenues for applications in reliability theory, economics, and applied probability.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"233 ","pages":"Article 110663"},"PeriodicalIF":0.7,"publicationDate":"2026-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146191122","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 : 2026-02-02DOI: 10.1016/j.spl.2026.110666
Kuan Sun, Zhiguo Xiao
We propose a new method for estimating the effect of a continuous treatment when data contains unobserved group-level differences. Our approach uses group-level averages of treatments and covariates as “group balancing statistics” to eliminate differences between groups. We introduce the Group Balancing Generalized Propensity Score Matching (GBGPSM) estimator, establish its asymptotic properties, and evaluate its performance through simulations.
{"title":"Group balancing generalized propensity score matching with continuous treatments","authors":"Kuan Sun, Zhiguo Xiao","doi":"10.1016/j.spl.2026.110666","DOIUrl":"10.1016/j.spl.2026.110666","url":null,"abstract":"<div><div>We propose a new method for estimating the effect of a continuous treatment when data contains unobserved group-level differences. Our approach uses group-level averages of treatments and covariates as “group balancing statistics” to eliminate differences between groups. We introduce the Group Balancing Generalized Propensity Score Matching (GBGPSM) estimator, establish its asymptotic properties, and evaluate its performance through simulations.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"233 ","pages":"Article 110666"},"PeriodicalIF":0.7,"publicationDate":"2026-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146191126","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 : 2026-01-30DOI: 10.1016/j.spl.2026.110662
Vera Djordjilović , Tamar Sofer , Jonathan M. Dreyfuss
Directional replicability addresses the question of whether an effect studied across independent studies is present with the same direction in at least of them, for . When the expected direction of the effect is not specified in advance, the state of the art recommends assessing replicability separately by combining one-sided -values for both directions (left and right), and then doubling the smaller of the two resulting combined -values to account for multiple testing. In this work, we show that this multiplicative correction is not always necessary, and give a sufficient and necessary condition under which it can be safely omitted.
{"title":"Directional replicability: When can the factor of two be omitted","authors":"Vera Djordjilović , Tamar Sofer , Jonathan M. Dreyfuss","doi":"10.1016/j.spl.2026.110662","DOIUrl":"10.1016/j.spl.2026.110662","url":null,"abstract":"<div><div>Directional replicability addresses the question of whether an effect studied across <span><math><mi>n</mi></math></span> independent studies is present with the same direction in at least <span><math><mi>r</mi></math></span> of them, for <span><math><mrow><mi>r</mi><mo>≥</mo><mn>2</mn></mrow></math></span>. When the expected direction of the effect is not specified in advance, the state of the art recommends assessing replicability separately by combining one-sided <span><math><mi>p</mi></math></span>-values for both directions (left and right), and then doubling the smaller of the two resulting combined <span><math><mi>p</mi></math></span>-values to account for multiple testing. In this work, we show that this multiplicative correction is not always necessary, and give a sufficient and necessary condition under which it can be safely omitted.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"233 ","pages":"Article 110662"},"PeriodicalIF":0.7,"publicationDate":"2026-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146191123","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 : 2026-01-30DOI: 10.1016/j.spl.2026.110665
Zhi Li , Dennis K.J. Lin , Zhiming Li
This paper introduces a blocked general minimum lower-order confounding (B-GMC) criterion and focuses on constructing optimal three-level blocked designs. We obtain some necessary conditions for constructing B-GMC designs. In addition, all 27-run and some 81-run B-GMC designs are tabulated.
{"title":"Optimal three-level blocked designs via general minimum lower-order confounding criterion","authors":"Zhi Li , Dennis K.J. Lin , Zhiming Li","doi":"10.1016/j.spl.2026.110665","DOIUrl":"10.1016/j.spl.2026.110665","url":null,"abstract":"<div><div>This paper introduces a blocked general minimum lower-order confounding (B-GMC) criterion and focuses on constructing optimal three-level blocked designs. We obtain some necessary conditions for constructing B-GMC designs. In addition, all 27-run and some 81-run B-GMC designs are tabulated.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"233 ","pages":"Article 110665"},"PeriodicalIF":0.7,"publicationDate":"2026-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146190587","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 : 2026-01-30DOI: 10.1016/j.spl.2026.110667
Fengli Song, Yurong Zhang, Zhou Wang, Peng Lai
We introduce two transfer learning algorithms based on the single-index model, tailored for settings where the transferable data are either known or unknown. Theoretical properties of the proposed models are discussed. Their performance is evaluated through numerical simulations and applied to Genotype-Tissue Expression data.
{"title":"Transfer learning based on the single-index model","authors":"Fengli Song, Yurong Zhang, Zhou Wang, Peng Lai","doi":"10.1016/j.spl.2026.110667","DOIUrl":"10.1016/j.spl.2026.110667","url":null,"abstract":"<div><div>We introduce two transfer learning algorithms based on the single-index model, tailored for settings where the transferable data are either known or unknown. Theoretical properties of the proposed models are discussed. Their performance is evaluated through numerical simulations and applied to Genotype-Tissue Expression data.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"233 ","pages":"Article 110667"},"PeriodicalIF":0.7,"publicationDate":"2026-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146191119","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}
This article examines the robustness of maximum likelihood estimators in Poisson integer-valued autoregressive processes of order one, which model count time series with autocorrelation and Poisson-distributed innovations. While maximum likelihood estimation is widely used to estimate the autocorrelation parameter and the mean parameter , its sensitivity to outliers and model deviations remains insufficiently understood. We use influence function theory to quantify the local impact of infinitesimal contamination on the estimators and compute gross error sensitivity to assess worst-case sensitivity. The methodology connects robust statistical ideas with count time series modeling by providing explicit score expressions and estimating Fisher information by simulation under stationarity. Visual diagnostics, including heatmaps, three-dimensional sensitivity surfaces, and summary tables, identify parameter regimes where the estimators become vulnerable to contamination. The study provides practical guidance and diagnostics for applied researchers in the social sciences and epidemiology.
{"title":"On the robustness of maximum likelihood estimators for the Poisson INAR(1) model","authors":"Subhankar Chattopadhyay , Sancharee Basak , Atanu Biswas","doi":"10.1016/j.spl.2026.110659","DOIUrl":"10.1016/j.spl.2026.110659","url":null,"abstract":"<div><div>This article examines the robustness of maximum likelihood estimators in Poisson integer-valued autoregressive processes of order one, which model count time series with autocorrelation and Poisson-distributed innovations. While maximum likelihood estimation is widely used to estimate the autocorrelation parameter <span><math><mi>α</mi></math></span> and the mean parameter <span><math><mi>λ</mi></math></span>, its sensitivity to outliers and model deviations remains insufficiently understood. We use influence function theory to quantify the local impact of infinitesimal contamination on the estimators and compute gross error sensitivity to assess worst-case sensitivity. The methodology connects robust statistical ideas with count time series modeling by providing explicit score expressions and estimating Fisher information by simulation under stationarity. Visual diagnostics, including heatmaps, three-dimensional sensitivity surfaces, and summary tables, identify parameter regimes where the estimators become vulnerable to contamination. The study provides practical guidance and diagnostics for applied researchers in the social sciences and epidemiology.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"233 ","pages":"Article 110659"},"PeriodicalIF":0.7,"publicationDate":"2026-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146039474","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 : 2026-01-23DOI: 10.1016/j.spl.2026.110660
Ruizhe Hu , Huojun Wu
This paper establishes the strong exponential turnpike property for a partially observed stochastic linear–quadratic optimal control problem. We apply an orthogonal decomposition method to decouple the system into filtering and difference processes. Under standard stabilizability and detectability conditions, the convergence of the difference process is proven, leading to the exponential turnpike property with explicitly characterized decay rates. These rates are shown to be governed by the convergence rate between the two decoupled processes.
{"title":"Turnpike properties for stochastic linear–quadratic optimal control problems with partial observation","authors":"Ruizhe Hu , Huojun Wu","doi":"10.1016/j.spl.2026.110660","DOIUrl":"10.1016/j.spl.2026.110660","url":null,"abstract":"<div><div>This paper establishes the strong exponential turnpike property for a partially observed stochastic linear–quadratic optimal control problem. We apply an orthogonal decomposition method to decouple the system into filtering and difference processes. Under standard stabilizability and detectability conditions, the convergence of the difference process is proven, leading to the exponential turnpike property with explicitly characterized decay rates. These rates are shown to be governed by the convergence rate between the two decoupled processes.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"233 ","pages":"Article 110660"},"PeriodicalIF":0.7,"publicationDate":"2026-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146080732","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 : 2026-01-20DOI: 10.1016/j.spl.2026.110658
Francesco Bravo
This paper proposes a new simple test for model selection between two possibly misspecified competing semiparametric models. An important feature of the test is that it controls uniformly its size regardless as to whether the competing models are nested, overlapping or non nested and can be applied to overidentified models with weakly dependent observations.
{"title":"A uniform model selection test for semiparametric models","authors":"Francesco Bravo","doi":"10.1016/j.spl.2026.110658","DOIUrl":"10.1016/j.spl.2026.110658","url":null,"abstract":"<div><div>This paper proposes a new simple test for model selection between two possibly misspecified competing semiparametric models. An important feature of the test is that it controls uniformly its size regardless as to whether the competing models are nested, overlapping or non nested and can be applied to overidentified models with weakly dependent observations.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"232 ","pages":"Article 110658"},"PeriodicalIF":0.7,"publicationDate":"2026-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146023410","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 : 2026-01-20DOI: 10.1016/j.spl.2026.110654
Guillaume Chauvet , Mathieu Gerber
In this work, we introduce an approach based on the martingale representation of a sampling design and Azuma–Hoeffding’s inequality to derive exponential inequalities for the difference between a Horvitz–Thompson estimator and its expectation. We derive a new exponential inequality for conditionally negatively associated (CNA) sampling designs, which is shown to improve over two existing inequalities that can be used in this context. We establish that Chao’s procedure, Tillé’s elimination procedure and the generalized Midzuno method are CNA sampling designs, and thus obtain an exponential inequality for these three sampling procedures. We show that our approach is useful beyond CNA sampling designs by deriving an exponential inequality for Brewer’s method.
{"title":"Exponential inequalities for sampling designs","authors":"Guillaume Chauvet , Mathieu Gerber","doi":"10.1016/j.spl.2026.110654","DOIUrl":"10.1016/j.spl.2026.110654","url":null,"abstract":"<div><div>In this work, we introduce an approach based on the martingale representation of a sampling design and Azuma–Hoeffding’s inequality to derive exponential inequalities for the difference between a Horvitz–Thompson estimator and its expectation. We derive a new exponential inequality for conditionally negatively associated (CNA) sampling designs, which is shown to improve over two existing inequalities that can be used in this context. We establish that Chao’s procedure, Tillé’s elimination procedure and the generalized Midzuno method are CNA sampling designs, and thus obtain an exponential inequality for these three sampling procedures. We show that our approach is useful beyond CNA sampling designs by deriving an exponential inequality for Brewer’s method.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"232 ","pages":"Article 110654"},"PeriodicalIF":0.7,"publicationDate":"2026-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146023411","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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