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Lower bounds for the trade-off between bias and mean absolute deviation 偏差与平均绝对偏差之间权衡的下限
IF 0.8 4区 数学 Q3 STATISTICS & PROBABILITY Pub Date : 2024-06-13 DOI: 10.1016/j.spl.2024.110182
Alexis Derumigny , Johannes Schmidt-Hieber

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 f in a class of β-Hölder smooth functions. Let ’worst-case’ refer to the supremum over all functions f in the Hölder class. It is shown that any estimator with worst-case bias nβ/(2β+1)ψn must necessarily also have a worst-case mean absolute deviation that is lower bounded by ψn. To derive the result, we establish abstract inequalities relating the change of expectation for two probability measures to the mean absolute deviation.

在非参数统计中,最优估计率通常会兼顾偏差和随机误差。最近关于超参数化的研究提出了一个问题:是否存在不服从这种权衡的最优估计率?在本研究中,我们将考虑在高斯白噪声模型中,用一类 β-Hölder 平滑函数中的回归函数 f 进行点估计。让 "最坏情况 "指的是 Hölder 类中所有函数 f 的上集。结果表明,任何具有最坏情况偏差≲n-β/(2β+1)≕ψn 的估计器,其最坏情况平均绝对偏差的下限必然也是≳ψn。为了推导出这一结果,我们建立了有关两个概率度量的期望变化与平均绝对偏差的抽象不等式。
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引用次数: 0
Weak approximation of Schrödinger–Föllmer diffusion 薛定谔-福尔摩扩散的弱近似值
IF 0.8 4区 数学 Q3 STATISTICS & PROBABILITY Pub Date : 2024-06-07 DOI: 10.1016/j.spl.2024.110171
Koya Endo, Yumiharu Nakano

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.

我们考虑了薛定谔-福尔摩扩散的欧拉-丸山近似的弱收敛性,它是薛定谔桥问题的解,可用于从给定分布中采样。我们证明,在温和的正则性条件下,时间离散化过程的末端随机变量的分布会弱收敛于目标分布。
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引用次数: 0
On Yu and Hoff’s confidence intervals for treatment means 关于余和霍夫的治疗均值置信区间
IF 0.8 4区 数学 Q3 STATISTICS & PROBABILITY Pub Date : 2024-06-06 DOI: 10.1016/j.spl.2024.110170
Paul Kabaila

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.

Yu 和 Hoff 为单向布局中的处理均值构建了新的置信区间。他们使用半贝叶斯分析法评估了这些区间的预期长度。我们采用完全频数分析法对这些预期长度进行了揭示性评估。
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引用次数: 0
Short cycles of random permutations with cycle weights: Point processes approach 有周期权重的随机排列的短周期:点过程方法
IF 0.8 4区 数学 Q3 STATISTICS & PROBABILITY Pub Date : 2024-06-05 DOI: 10.1016/j.spl.2024.110169
Oleksii Galganov , Andrii Ilienko

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 {1,,n}. 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 n for a wide range of cycle weights. As an application, we give several limit theorems for various statistics of cycles.

我们研究具有周期权重的随机排列的短周期渐近行为。更具体地说,在一个特殊构造的度量空间上,其元素编码了所有可能的循环,我们考虑的点过程包含了{1,...,n}上给定随机排列的循环的所有信息。本文的主要结果是,在很大的循环权重范围内,上述过程的模糊拓扑在 n→∞ 时向泊松点过程的分布收敛。作为应用,我们给出了各种循环统计的几个极限定理。
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引用次数: 0
On negative correlation of Arboreal Gas for specific parameters 关于树栖气体与特定参数的负相关关系
IF 0.8 4区 数学 Q3 STATISTICS & PROBABILITY Pub Date : 2024-06-04 DOI: 10.1016/j.spl.2024.110174
Xiangyu Huang

Arboreal Gas is a type of (unrooted) random forest on a graph, where the probability is determined by a parameter β>0 per edge. This model can be considered as the limit of the q-states random cluster model with p=βq as q0. 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.

Arboreal Gas 是一种图上的(无根)随机森林,其概率由每条边的参数 β>0 决定。该模型可视为 q→0 时 p=βq 的 q 态随机簇模型的极限。当图的大小达到无穷大时,自然会产生一个关于 Arboreal Gas 弱极限的存在和性能的问题。这个问题的答案取决于 Arboreal Gas 的负相关,而这仍是一个未决问题。本文主要关注 Arboreal Gas 的负相关性,并提供了一些特定参数的结果。
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引用次数: 0
Exact quantiles of Gaussian process extremes 高斯过程极值的精确定量
IF 0.8 4区 数学 Q3 STATISTICS & PROBABILITY Pub Date : 2024-06-04 DOI: 10.1016/j.spl.2024.110173
Lijian Yang

Under nearly minimal conditions, continuity of extreme distribution function is established for both continuous Gaussian processes and finite Gaussian sequences, which entails existence of exact quantiles at any level. Also proved under simple conditions is strict monotonicity of extreme distribution functions that ensures uniqueness of exact quantiles at any level. These results provide convenient tools for developing statistical theory about global inference on functions.

在近乎最小的条件下,为连续高斯过程和有限高斯序列建立了极值分布函数的连续性,这意味着在任何水平上都存在精确的量值。在简单条件下,还证明了极值分布函数的严格单调性,确保了任何水平上精确量值的唯一性。这些结果为发展有关函数全局推断的统计理论提供了方便的工具。
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引用次数: 0
Exponential ergodicity for reflected SDEs with interaction in a multidimensional general domain 多维一般域中具有交互作用的反射自变量的指数遍历性
IF 0.8 4区 数学 Q3 STATISTICS & PROBABILITY Pub Date : 2024-06-04 DOI: 10.1016/j.spl.2024.110168
Ping Chen , Tusheng Zhang

In this paper, we consider reflected stochastic differential equations (SDEs) with interaction in a multidimensional general domain. The well-posedness is established under a monotone condition, and the exponential ergodicity is derived in the Wasserstein distance.

在本文中,我们考虑了多维一般域中具有交互作用的反射随机微分方程(SDE)。在单调条件下建立了良好求解性,并在 Wasserstein 距离中推导出指数遍历性。
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引用次数: 0
Isotropic random tangential vector fields on spheres 球面上的各向同性随机切向矢量场
IF 0.8 4区 数学 Q3 STATISTICS & PROBABILITY Pub Date : 2024-06-03 DOI: 10.1016/j.spl.2024.110172
Tianshi Lu

In this paper we characterized isotropic random tangential vector fields on d-spheres for d1 by the cross-covariance, and derived their Karhunen–Loève expansion. The tangential vector field can be decomposed into a curl-free part and a divergence-free part by the Helmholtz–Hodge decomposition. We proved that the two parts can be correlated on a 2-sphere, while they must be uncorrelated on a d-sphere for d3. On a 3-sphere, the divergence-free part can be further decomposed into two isotropic flows.

在本文中,我们通过交叉协方差描述了 d≥1 时 d 球上各向同性随机切向矢量场的特征,并推导出了它们的卡尔胡宁-洛夫展开(Karhunen-Loève expansion)。切向矢量场可以通过亥姆霍兹-霍奇分解分解为无卷曲部分和无发散部分。我们证明了这两部分在 2 球面上可以相关,而在 d≥3 的 d 球面上必须不相关。在 3 球面上,无发散部分可以进一步分解为两个各向同性流。
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引用次数: 0
Rate of convergence of trinomial formula to Black–Scholes formula 三项式公式与布莱克-斯科尔斯公式的收敛速度
IF 0.8 4区 数学 Q3 STATISTICS & PROBABILITY Pub Date : 2024-06-01 DOI: 10.1016/j.spl.2024.110167
Yuttana Ratibenyakool , Kritsana Neammanee

The Black–Scholes formula which was introduced by three economists, Black et al. (1973) has been widely used to calculate the theoretical price of the European call option. In 1979, Cox, Ross and Rubinstein (Cox et al., 1979) gave the binomial formula which is a tool to find the price of European option and showed that this formula converges to the Black–Scholes formula as the number of periods (n) converges to infinity. In 1988, Boyle investigated another formula that is used to find the price of European option, that is the trinomial formula. In 2015, Puspita et al. gave examples to show that the trinomial formula is closed to the Black–Scholes formula. After that, Ratibenyakool and Neammanee (2020) gave the rigorous proof of this convergence. In this paper, we show that the rate of convergence is of order 1n.

Black 等人(1973 年)提出的 Black-Scholes 公式被广泛用于计算欧式看涨期权的理论价格。1979 年,Cox、Ross 和 Rubinstein(Cox et al.,1979 年)给出了二项式公式,这是一种计算欧式期权价格的工具,并表明当期数(n)趋近于无穷大时,该公式与 Black-Scholes 公式趋同。1988 年,Boyle 研究了另一个用于计算欧式期权价格的公式,即三项式公式。2015 年,Puspita 等人举例说明了三项式公式与 Black-Scholes 公式是封闭的。之后,Ratibenyakool 和 Neammanee(2020 年)给出了这种收敛性的严格证明。在本文中,我们证明了收敛速率为 1n 阶。
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引用次数: 0
Some new asymptotic results for series estimation under clustered dependence 聚类依赖条件下序列估计的一些新渐近结果
IF 0.8 4区 数学 Q3 STATISTICS & PROBABILITY Pub Date : 2024-05-28 DOI: 10.1016/j.spl.2024.110156
Pingbo Hu , Xiuyuan Peng , Xinglin Hu

This paper presents some asymptotic results for series estimation of a nonparametric regression model under clustered dependence. A mean square rate of convergence for the series regression estimator is established. Moreover, asymptotic pointwise normality is shown for the series estimator.

本文提出了聚类依赖下非参数回归模型序列估计的一些渐近结果。本文确定了序列回归估计器的均方收敛率。此外,还证明了序列估计器的渐近点正态性。
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Statistics & Probability Letters
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