Statistics & Probability Letters最新文献

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Lower bounds for density estimation on symmetric spaces

IF 0.9 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters

Pub Date : 2025-03-31 DOI: 10.1016/j.spl.2025.110416

Dena Marie Asta

We prove that kernel density estimation on symmetric spaces of non-compact type, whose

L_{2}

-risk was bounded above in previous work (Asta, 2021), in fact achieves a minimax rate of convergence. With this result, the story for kernel density estimation on all symmetric spaces is completed. The idea in adapting the proof for Euclidean space is to suitably abstract vector space operations on Euclidean space to both actions of symmetric groups and reparametrizations of Helgason–Fourier transforms and to use the fact that the exponential map for symmetric spaces of non-compact type defines a diffeomorphism.

引用次数: 0

Posterior model consistency in high-dimensional Bayesian variable selection with arbitrary priors

IF 0.9 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters

Pub Date : 2025-03-28 DOI: 10.1016/j.spl.2025.110415

Min Hua , Gyuhyeong Goh

In the context of Bayesian regression modeling, posterior model consistency provides frequentist validation for Bayesian variable selection. A question that has long been open is whether posterior model consistency holds under arbitrary priors when high-dimensional variable selection is performed. In this paper, we aim to give an answer by establishing sufficient conditions for priors under which the posterior model distribution converges to a degenerate distribution at the true model. Our framework considers high-dimensional regression settings where the number of potential predictors grows at a rate faster than the sample size. We demonstrate that a wide selection of priors satisfy the conditions that we establish in this paper.

引用次数: 0

The impact of contamination and correlated design on the Lasso: An average case analysis

IF 0.9 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters

Pub Date : 2025-03-28 DOI: 10.1016/j.spl.2025.110417

Stanislav Minsker , Yiqiu Shen

We study the prediction problem in the context of the high-dimensional linear regression model. We focus on the practically relevant framework where a fraction of the linear measurements is corrupted while the columns of the design matrix can be moderately correlated. Our findings suggest that for most sparse signals, the Lasso estimator admits strong performance guarantees under more easily verifiable and less stringent assumptions on the design matrix compared to much of the existing literature.

引用次数: 0

Solution to a generalized FBSDE with delay and anticipated terms and applications to control problem with time-varying delay

IF 0.9 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters

Pub Date : 2025-03-25 DOI: 10.1016/j.spl.2025.110414

Yuecai Han , Yuhang Li , Zheng Li

In this paper, motivated by optimal control problem with time-varying delay, we study a type of generalized forward–backward stochastic differential equation. Both delay and anticipated terms appear in both forward equation and backward equation. The existence and uniqueness of the solution is obtained. As an application, the linear quadratic optimal control problem, where both state process and control process contain time-varying delay, is solved.

本文受具有时变延迟的最优控制问题的启发，研究了一种广义的前向后向随机微分方程。延迟项和预期项同时出现在前向方程和后向方程中。我们得到了解的存在性和唯一性。作为应用，我们解决了状态过程和控制过程都包含时变延迟的线性二次优化控制问题。

引用次数: 0

A novel approach for estimating multi-attribute Gaussian copula graphical models

IF 0.9 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters

Pub Date : 2025-03-24 DOI: 10.1016/j.spl.2025.110413

Lijie Li , Yang Yu , Wanfeng Liang , Feng Zou

This paper considers estimating multi-attribute Gaussian copula graphical models where each node represents multivariate variables with rich meanings. A two-stage semiparametric method is proposed to achieve modeling flexibility and estimation robustness simultaneously by utilizing normal score transformation. We derive the consistency of the proposed estimator under the spectral norm, and establish the theoretical guarantees on sparsistency under some mild conditions. Simulation studies and a real data example are provided to demonstrate the empirical performance of the proposed method. We provide the complete code supporting this article at https://github.com/JerryLi-Stat/Multi-attribute-GCGM.

本文考虑了多属性高斯协方图模型的估计问题，其中每个节点代表具有丰富含义的多变量。本文提出了一种两阶段半参数方法，利用正态分数变换同时实现建模灵活性和估计鲁棒性。我们推导了所提出的估计器在谱规范下的一致性，并在一些温和条件下建立了稀疏性的理论保证。我们还提供了仿真研究和真实数据示例，以证明所提方法的经验性能。我们在 https://github.com/JerryLi-Stat/Multi-attribute-GCGM 上提供了支持本文的完整代码。

引用次数: 0

Transportation cost inequalities for the stochastic Ginzburg–Landau equation driven by space–time white noises

IF 0.9 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters

Pub Date : 2025-03-24 DOI: 10.1016/j.spl.2025.110409

Beibei Zhang

In this paper, we establish transportation cost inequalities for the solution of the stochastic complex Ginzburg–Landau equation driven by a space–time white noise on the spaces

L^{2} ([0, T] \times D)

C ([0, T]; L^{2} (D))

. The proof is based on the estimates of the nonlinear term.

引用次数: 0

The local long-time behaviour for continuous-time branching processes

IF 0.9 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters

Pub Date : 2025-03-24 DOI: 10.1016/j.spl.2025.110412

Liuyan Li , Junping Li

Let

{Z (t); t \geq 0}

be a continuous-time branching process. There is a normalizing function

γ_{t}

such that

Z (t) γ_{t}

converges almost surely to a random variable. In this paper, we obtain a local limit theorem for

{Z (t); t \geq 0}

, which refers to the asymptotic behaviour of

P (Z (t) = k_{t})

with

lim_{t \to \infty} k_{t} γ_{t} = x

and

x > 0

. This expands the existing results of the discrete-time branching processes.

引用次数: 0

Weak limits of standardized sums of independent geometrically distributed random variables

IF 0.9 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters

Pub Date : 2025-03-23 DOI: 10.1016/j.spl.2025.110410

José A. Adell

We consider standardized sums of independent geometrically distributed random variables whose failure probabilities approach the unity. We show that such sums converge in law to a random variable having an infinitely divisible distribution whose characteristic function depends on the values of the Riemann zeta function at integer arguments. This is motivated by a probabilistic representation of the Stirling numbers of the second kind.

引用次数: 0

Asymptotic normality of the Conditional Value-at-Risk based Pickands estimator

IF 0.9 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters

Pub Date : 2025-03-21 DOI: 10.1016/j.spl.2025.110411

Yizhou Li , Paweł Polak

We show weak convergence of the empirical Conditional Value-at-Risk (CVaR) in functional space and the asymptotic normality of the CVaR-based Pickands estimator from Chen (2021). These results demonstrate that the CVaR-based estimator has significantly lower asymptotic variance than analogous VaR-based constructions.

引用次数: 0

Construction of designs with space-filling and orthogonal property

IF 0.9 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters

Pub Date : 2025-03-19 DOI: 10.1016/j.spl.2025.110408

Min Li , Yuan Feng , Xiao Wang , Weiping Zhou

Space-filling designs are widely used in computer experiments, but their construction presents significant challenges. This paper introduces novel methods for generating maximin distance Latin hypercube designs (LHDs) and space-filling balanced designs with a slice structure, removing the reliance on computational searches. We also offer a simple yet effective approach to constructing sliced Latin hypercube designs (SLHDs), which achieve space-filling in each slice and maintain good orthogonality and stratification properties across the entire design. The resulting designs are more space-filling than existing designs.

空间填充设计在计算机实验中得到广泛应用，但其构造却面临巨大挑战。本文介绍了生成最大距离拉丁超立方设计（LHD）和具有切片结构的空间填充平衡设计的新方法，从而消除了对计算搜索的依赖。我们还提供了一种简单而有效的方法来构建切片拉丁超立方设计（SLHD），这种设计可以在每个切片中实现空间填充，并在整个设计中保持良好的正交性和分层特性。由此产生的设计比现有设计更能填充空间。

引用次数: 0

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