JournalTOCs

Communications in Mathematics and Statistics
Journal Prestige (SJR): 0.556

Citation Impact (citeScore): 1
Number of Followers: 3

Hybrid journal (It can contain Open Access articles)
ISSN (Print) 2194-6701 - ISSN (Online) 2194-671X
Published by Springer-Verlag

[2468 journals]

Stability of the Two-Dimensional Point Vortices in Euler Flows
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  Abstract: We consider the two-dimensional incompressible Euler equation $$\begin{aligned}{\left\{ \begin{array}{ll} \partial _t \omega + u\cdot \nabla \omega =0, \\ \omega (x,0)=\omega _0(x). \end{array}\right. }\end{aligned}$$ ∂ t ω + u · ∇ ω = 0 , ω ( x , 0 ) = ω 0 ( x ) . We are interested in the cases when the initial vorticity has the form $$\omega _0=\omega _{0,\epsilon }+\omega _{0p,\epsilon }$$, where $$\omega _{0,\epsilon }$$ is concentrated near M disjoint points $$p_m^0$$ and $$\omega _{0p,\epsilon }$$ is a small perturbation term. We prove that for such initial vorticities, the solution $$\omega (x,t)$$ admits a decomposition $$\omega (x,t)=\omega _{\epsilon }(x,t)+\omega _{p,\epsilon }(x,t)$$, where $$\omega _{\epsilon }(x,t)$$ remains concentrated near M points $$p_m(t)$$ and $$\omega _{p,\epsilon }(x,t)$$ remains small for $$t \in [0,T]$$. As a consequence of such decomposition, we are able to consider the initial vorticity of the form $$\omega _0(x)=\sum _{m=1}^M \frac{\gamma _m}{\epsilon ^2}\eta (\frac{x-p_m^0}{\epsilon })$$, where we do not assume $$\eta $$ to have compact support. Finally, we prove that if $$p_m(t)$$ remains separated for all $$t\in [0,+\infty )$$, then $$\omega (x,t)$$ remains concentrated near M points at least for $$t \le c_0 \log A_{\epsilon } $$, where $$A_{\epsilon }$$ is small and converges to 0 as $$\epsilon \rightarrow 0$$.
  PubDate: 2025-06-13
Asymptotic Stability for Non-equicontinuous Markov Semigroups
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  Abstract: We prove that the asymptotic stability, also known as the weak mixing, is equivalent to a lower bound condition together with the eventual continuity. The latter is a form of weak regularity for Markov–Feller semigroups that generalizes the e-property. Additionally, we provide an example of an asymptotically stable Markov semigroup with essential randomness that does not satisfy the e-property.
  PubDate: 2025-06-09
A General Class of Transformation Cure Rate Frailty Models for
Multivariate Interval-Censored Data
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  Abstract: The promotion time or non-mixture cure model is a popular tool for analyzing failure time data with a cured fraction and its usefulness in survival analysis has been well recognized. Although a number of inference procedures under this model have been proposed for univariate interval-censored data, corresponding estimation methods under multivariate interval censoring are still undeveloped because of the challenges in maximizing the observed data likelihood function with complex form. In this paper, we investigate the inference procedure for a class of generalized promotion time cure models, namely transformation cure rate frailty models, with multivariate interval-censored data. The class of models is quite flexible and general and includes the proportional hazards and proportional odds cure rate frailty models as special cases. An expectation-maximization algorithm is developed to calculate the nonparametric maximum likelihood estimators, and the asymptotic properties of the obtained estimators are derived with the empirical process techniques. Extensive simulation studies demonstrate the reliable and satisfactory empirical performance of the proposed method. It is then applied to a set of sexually transmitted infection data arising from an epidemiological study for illustration.
  PubDate: 2025-05-27
On the Robust Nonparametric Regression Estimate in the Single Functional
Index Model
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  Abstract: In this work, we construct and study a family of robust nonparametric estimators for a regression function based on kernel methods. The data are functional, independent and identically distributed, and are linked to a single-index model. Under general conditions, we establish the pointwise and uniform almost complete convergence, as well as the asymptotic normality of the estimator. We explicitly derive the asymptotic variance and, as a result, provide confidence bands for the theoretical parameter. A simulation study is conducted to illustrate the proposed methodology.
  PubDate: 2025-05-24
The Optimization Problem for Functions of Bounded Variation
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  Abstract: For a function of bounded variation f in $$\mathbb {R}^n$$, we consider the optimization problem of affine total variation, subject to a constraint on the LYZ body $$\langle f\rangle $$ under affine transformations, along with its dual problem. As applications, we also derive properties of the solutions to the related optimization problem, as well as properties of the LYZ body.
  PubDate: 2025-05-23
Global Existence and Uniqueness of Pathwise Solution to the Stochastic 2D
Inviscid Boussinesq Equations
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  Abstract: Global well-posedness of 2D inviscid Boussinesq equations is unsolved. In the present work, we find that if this inviscid hydrodynamics equation is perturbed by noise, the global well-posedness holds in high probability with initial data satisfies a certain Gevrey-type bound. Moreover, the unique global solution to the stochastic inviscid 2D Boussinesq equation is bounded by the initial data.
  PubDate: 2025-05-21
A New Class of IMSE-Based Criteria for Optimal Designs in Multi-response
Random Coefficient Regression Models
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  Abstract: A new class of criteria for optimal designs in random coefficient regression (RCR) models with r responses is presented, which is based on the integrated mean squared error (IMSE) for the prediction of random effects. This class, referred to as $$\textrm{IMSE}_{r,L}$$-class of criteria, is invariant with respect to different parameterizations of the model and contains $$\textrm{IMSE}$$- and G-optimality as special cases for the prediction in univariate response situations. General equivalence theorems for $$\textrm{IMSE}_{r,L}$$-criteria are established for $$L\in [1,\infty )$$ and $$L=\infty $$, respectively, which are used to check $$\textrm{IMSE}_{r,L}$$-optimality of designs. $$\textrm{IMSE}_{r,L}$$-optimal designs for linear and quadratic bi-response RCR models are given for illustration.
  PubDate: 2025-05-18
Testing Equality of Two High-Dimensional Correlation Matrices
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  Abstract: This paper is concerned with testing the equality of two high-dimensional Pearson correlation matrices without any structural assumption under normal populations. A U-statistic based on the Frobenius norm of the difference between two transformational correlation matrices is proposed for testing the equality of two correlation matrices when both sample sizes and dimension tend to infinity. And the asymptotic normality of the proposed testing statistic is also derived under the null and alternative hypotheses. Moreover, the asymptotic power function is also presented. Simulation studies show that the proposed test performs very well in a wide range of settings and can be allowed for the case of large dimensions and small sample sizes.
  PubDate: 2025-05-16
Limit Behavior of Deformed Hermitian–Yang–Mills Metrics on
Kähler Surfaces
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  Abstract: In this paper, we consider the limit behavior of a sequence of deformed Hermitian–Yang–Mills metrics $$F_m$$ on $$L^{\otimes m}$$ where L is an ample line bundle over a Kähler surface $$(X, \omega )$$. If the cohomology class $$c_1(L)$$ admits a solution of the J-equation, then we prove that $$F_m$$ will converge to it. Furthermore, we also consider a boundary case. In this case, we prove that $$F_m$$ will converge to a singular Kähler metric away from a finite number of curves with negative self-intersection on the surface.
  PubDate: 2025-05-14
Smoothness of the Optimal Transport Map on Riemannian Products of Spheres
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  Abstract: This paper approaches the smoothness of the optimal transport map on Riemannian products manifolds. By classical continuity method, we give an alternative proof of the smoothness of the optimal transport map on Riemannian products of the round spheres. In addition, we also prove that the smoothness of the optimal transport map is not stable in Riemannian products of round spheres.
  PubDate: 2025-05-13
Consumption–Investment and Reinsurance Problem Under Markovian Regime
Switching: Time-Consistent Solution
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  Abstract: This paper presents a characterization of equilibrium in a game theoretic description of discounting stochastic consumption, investment and reinsurance problem, in which the controlled state process evolves according to a multi-dimensional linear stochastic differential equation, when the noise is driven by a Brownian motion under the effect of a Markovian regime switching. The running and the terminal costs in the objective functional, are explicitly depended on some general discount functions, which create the time inconsistency of the considered model. Open-loop Nash equilibrium controls are described through some necessary and sufficient equilibrium conditions as well as a verification result. A state feedback equilibrium strategy is achieved via certain partial differential-difference equation. As an application, we study an investment–consumption and equilibrium reinsurance/new business strategies for some particular cases of power and logarithmic utility functions. A numerical example is provided to demonstrate the efficacy of theoretical results.
  PubDate: 2025-05-12
Regression Analysis for Clustered Current Status Data Under Additive
Transformation Models
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  Abstract: This paper discusses regression analysis of clustered case I interval-censored data under a class of additive transformation risk models. We consider the situation that cluster size is informative about correlated failure times from the same cluster. A weighted estimating equation approach is constructed and the asymptotic properties are established. Finite-sample performance of the proposed method is assessed through a series of simulation studies. The results indicate that the proposed procedures work well and the weighted estimating equation method performs well in both the cases that cluster size is informative and noninformative. The proposed method is applied to analyze a real data set from a lung tumorigenicity study.
  PubDate: 2025-05-07
Testing High-Dimensional Means for Sparse Signals
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  Abstract: In this paper, we investigate the high-dimensional mean vector testing problem with fewer observations than the dimension. We revisit a kind of test which belongs to the supremum-type statistic and propose a novel test by the combination of the maximum and minimum values among all component tests. The asymptotic null distributions of two tests are obtained and the asymptotical powers against sparse alternatives are also investigated under weak conditions. Simulation results show that these two tests can control empirical sizes well. Our novel test can gain desirable powers. A real data example about Electro-Encephalo Gram measurements also demonstrates that our proposed test has desirable numerical performances.
  PubDate: 2025-05-05
Adaptive Robust and Efficient Variable Selection for Heterogeneous Data
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  Abstract: Penalized quantile regression can detect heteroscedasticity, and is robust to heavy-tailed errors. However, it could be less efficient than the penalized least squared regression when the error follows a normal distribution. To solve this problem, we propose a robust and efficient variable selection procedure via a convex combination of the penalized least squared regression and penalized quantile regression with data-driven weights. The proposed method can adapt to different error structures and automatically chooses the weight to achieve both robustness and high efficiency. Under some conditions, the asymptotic properties of our proposed estimators are established. Besides, we apply a minorization–maximization algorithm to solve the proposed optimization problem. Extensive numerical studies are carried out to compare the performances of our method and other existing methods, and the results reveal that the newly proposed method is equivalent to the penalized least squared regression when the error follows a normal distribution, can detect heteroscedasticity, and is robust to heavy-tailed errors including the infinite variance case. Finally, we present a real example for demonstration.
  PubDate: 2025-05-05
Sufficient Dimension Reduction for Multiple Compositional Predictors
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  Abstract: Motivated by research problems arising in the analysis of economic and geochemical data, we consider sufficient dimension reduction in regression with multiple compositional predictors. We develop a second-moment-based method that respects the unique features of compositional data. The proposed method is model-free and can fully recover the central dimension-reduction subspace, which then allows us to derive a sufficient reduction of the compositional predictors. In addition, we suggest a Bayesian-type information criterion to determine the structural dimension of the central subspace. Extensive simulation studies and an application to a disposable income of Chinese urban residents data set demonstrate the effectiveness and efficiency of the method.
  PubDate: 2025-04-25
Statistical inference for discretely observed fractional diffusion
processes with random effects
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  Abstract: We address statistical inference for linear fractional diffusion processes with random effects in the drift. In particular, we investigate maximum likelihood estimators (MLEs) of the random effect parameters. First of all, we estimate the Hurst parameter $$H\in (0,1)$$ from one single subject. Second, assuming that the Hurst index $$H\in (0,1)$$ is known, we derive the MLEs and examine their asymptotic behavior as the number of subjects under study becomes large, with random effects being normally distributed.
  PubDate: 2025-04-03
A trace Moser-Trudinger inequality on compact Riemannian surface with
corners on its boundary
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  Abstract: In this paper, we establish a trace Moser-Trudinger inequality on a compact Riemann surface $$\Sigma $$ with corners on $$\partial \Sigma $$. It is also regarded as “trace imbedding inequality” when the boundary carries the conical sigularities. Besides, based on blow-up analysis, we prove the existence of extremal functions for this trace Moser-Trudinger inequality.
  PubDate: 2025-04-03
Algebras Over a Symmetric Fusion Category and Integrations
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  Abstract: We study the symmetric monoidal 2-category of finite semisimple module categories over a symmetric fusion category. In particular, we study $$E_n$$-algebras in this 2-category and compute their $$E_n$$-centers for $$n=0,1,2$$. We also compute the factorization homology of stratified surfaces with coefficients given by $$E_n$$-algebras in this 2-category for $$n=0,1,2$$ satisfying certain anomaly-free conditions.
  PubDate: 2025-04-01
Decay of Geometry for a Class of Cubic Polynomials
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  Abstract: In this paper, we study a class of bimodal cubic polynomials for which its critical points have the same $$\omega $$-limit set which is an invariant Cantor set. These maps have generalized Fibonacci combinatorics in terms of generalized renormalization on the twin principal nest. It is proved that such maps possess ‘decay of geometry’ in the sense that the scaling factor of the twin principal nest decreases at least exponentially fast. As an application, we prove that they have no Cantor attractor.
  PubDate: 2025-04-01
A New Method for Simultaneous Estimation of Means of Two Sensitive
Variables Using Correlated Scrambling Variables
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  Abstract: Recently (Ahmed et al. in Stat Theory Methods 47:324–343, 2018) have discussed the problem of estimating the means of two sensitive variables simultaneously by using two uncorrelated scrambling variables. In this study, we introduce a new idea that use of correlated scrambling variables in randomized response techniques play an important role to increase the efficiency of the estimators of population means of sensitive variables. We found that the simultaneous estimation of the means of the two sensitive variables by using two correlated scrambling variables results in gain in the efficiency of the estimators. This idea is appealing because it costs nothing to the investigator and does not effect the privacy of a respondent as well. Empirical evidences are given based on application to a real secondary data set.
  PubDate: 2025-03-13

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