Journal of Statistical Planning and Inference最新文献

英文中文

Asymptotically efficient estimation under local constraint in Wicksell’s problem 局部约束下Wicksell问题的渐近有效估计

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Statistical Planning and Inference

Pub Date : 2025-05-16 DOI: 10.1016/j.jspi.2025.106299

Francesco Gili, Geurt Jongbloed, Aad van der Vaart

We consider nonparametric estimation of the distribution function

F

of squared sphere radii in the classical Wicksell problem. Under smoothness conditions on

F

in a neighborhood of

x

, in Gili et al. (2024) it is shown that the Isotonic Inverse Estimator (IIE) is asymptotically efficient and attains rate of convergence

\sqrt{n / log n}

. If

F

is constant on an interval containing

x

, the optimal rate of convergence increases to

\sqrt{n}

and the IIE attains this rate adaptively, i.e. without explicitly using the knowledge of local constancy. However, in this case, the asymptotic distribution is not normal. In this paper, we introduce three informed projection-type estimators of

F

, which use knowledge on the interval of constancy and show these are all asymptotically equivalent and normal. Furthermore, we establish a local asymptotic minimax lower bound in this setting, proving that the three informed estimators are asymptotically efficient and a convolution result showing that the IIE is not efficient. We also derive the asymptotic distribution of the difference of the IIE with the efficient estimators, demonstrating that the IIE is not asymptotically equivalent to the informed estimators. Through a simulation study, we provide evidence that the performance of the IIE closely resembles that of its competitors, supporting the use of the IIE as the standard choice when no information about

F

is available.

研究了经典Wicksell问题中平方球半径分布函数F的非参数估计。在x邻域F上的平滑条件下，Gili et al.（2024）证明了等压逆估计（IIE）是渐近有效的，其收敛速率为n/logn。如果F在包含x的区间上是常数，则最优收敛速率增加到n，并且IIE自适应地达到该速率，即不显式地使用局部常数的知识。然而，在这种情况下，渐近分布不是正态分布。本文引入了F的三个已知投影型估计，它们利用了关于常数区间的知识，证明了它们都是渐近等价的正态估计。在此基础上，我们建立了局部渐近极大极小下界，证明了这三个估计量是渐近有效的，并给出了一个卷积结果，证明了IIE是无效的。我们还推导了IIE与有效估计量之差的渐近分布，证明了IIE与知情估计量并不渐近等价。通过模拟研究，我们提供了证据，证明IIE的性能与其竞争对手非常相似，支持在没有关于F的信息时使用IIE作为标准选择。

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引用次数: 0

A nonparametric test for the heterogeneity of the spatial autoregressive parameter 空间自回归参数异质性的非参数检验

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Statistical Planning and Inference

Pub Date : 2025-05-10 DOI: 10.1016/j.jspi.2025.106298

Yangbing Tang , Jiang Du , Zhongzhan Zhang

We propose a new test for the heterogeneity of the spatial autoregressive parameter in semiparametric varying-coefficient spatial autoregressive models. Our specification test is built on the difference of parametric and nonparametric estimates of the spatial autoregressive coefficient, where the two estimates are obtained by the sieve GMM estimation method. Under mild conditions, we derive the limiting null distribution, the local power property and consistency of the test statistic. Numerical simulations show promising performance of the proposed test for finite samples in the considered cases, and the crime data of Tokyo is analyzed to illustrate the usefulness of the test.

本文提出了一种检验半参数变系数空间自回归模型中空间自回归参数异质性的新方法。我们的规范检验建立在空间自回归系数的参数和非参数估计的差异上，其中两个估计是通过筛选GMM估计方法获得的。在温和条件下，导出了检验统计量的极限零分布、局部功率性质和一致性。数值模拟结果表明，该方法在有限样本情况下具有良好的性能，并对东京的犯罪数据进行了分析，以说明该方法的有效性。

引用次数: 0

Copula-based semiparametric nonnormal transformed linear model for survival data with dependent censoring 基于copula的生存数据非正态变换线性模型

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Statistical Planning and Inference

Pub Date : 2025-05-07 DOI: 10.1016/j.jspi.2025.106296

Huazhen Yu , Lixin Zhang

Although the independent censoring assumption is commonly used in survival analysis, it can be violated when the censoring time is related to the survival time, which often happens in many practical applications. To address this issue, we propose a flexible semiparametric method for dependent censored data. Our approach involves fitting the survival time and the censoring time with a joint transformed linear model, where the transformed function is unspecified. This allows for a very general class of models that can account for possible covariate effects, while also accommodating administrative censoring. We assume that the transformed variables have a bivariate nonnormal distribution based on parametric copulas and parametric marginals, which further enhances the flexibility of our method. We demonstrate the identifiability of the proposed model and establish the consistency and asymptotic normality of the model parameters under appropriate regularity conditions and assumptions. Furthermore, we evaluate the performance of our method through extensive simulation studies, and provide a real data example for illustration.

虽然独立审查假设是生存分析中常用的假设，但是当审查时间与生存时间相关时，独立审查假设就会被违反，这种情况在许多实际应用中经常发生。为了解决这个问题，我们提出了一种灵活的半参数方法。我们的方法包括用一个联合变换的线性模型拟合生存时间和审查时间，其中变换的函数是未指定的。这允许一个非常一般的模型类别，可以解释可能的协变量效应，同时也适应行政审查。我们假设变换后的变量具有基于参数copula和参数边际的二元非正态分布，这进一步增强了方法的灵活性。我们证明了模型的可辨识性，并在适当的正则性条件和假设下，建立了模型参数的一致性和渐近正态性。此外，我们通过大量的仿真研究来评估我们的方法的性能，并提供了一个真实的数据示例来说明。

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引用次数: 0

Maximum Projection Gini Correlation (MaGiC) for mixed categorical and numerical data 混合分类和数值数据的最大投影基尼相关（MaGiC）

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Statistical Planning and Inference

Pub Date : 2025-04-24 DOI: 10.1016/j.jspi.2025.106294

Hong Xiao , Radhakrishna Adhikari , Yixin Chen , Xin Dang

We propose a projection correlation for measure of dependence between numerical multivariate variables and categorical variables. The projection correlation, defined as the maximum of the Gini correlations (i.e., MaGiC) between the categorical variable and the univariate projections of the multivariate vector, is non-parametric, and intuitively produces a high coefficient when the two variables are dependent, and zero when they are independent. We show that MaGiC possesses the property of nestedness, in that it is non-decreasing with the increasing number of features in the numerical vector, while remaining unchanged if additional numerical features are independent of the categorical variable and original features. We establish

\sqrt{n}

-consistency of the sample projection correlation. A powerful

K

-sample test can be carried out via the MaGiC-based independence test. When compared with related correlation definitions for multivariate variables, MaGiC also enjoys a faster implementation, with the computational complexity

O (m n (d + log n))

where

d

is the dimension of the numerical variable,

n

is the sample size, and

m

is the number of projections performed, as opposed to

O (d n^{2})

for Gini correlation. We demonstrate these properties through simulation and application to real datasets.

我们提出了一种投影相关性来衡量数值多元变量和分类变量之间的相关性。投影相关性，定义为类别变量与多元向量的单变量投影之间的基尼相关性（即MaGiC）的最大值，是非参数的，当两个变量相依时直观地产生高系数，当它们独立时产生零系数。我们证明了MaGiC具有嵌套性，即随着数值向量中特征数量的增加，它不减少，而如果附加的数值特征独立于分类变量和原始特征，它保持不变。我们建立了样本投影相关性的n一致性。通过基于magic的独立性检验，可以进行强大的k样本检验。与多元变量的相关关联定义相比，MaGiC的实现速度更快，计算复杂度为O(mn(d+logn))，其中d是数值变量的维度，n是样本量，m是执行的预测数量，而基尼相关的计算复杂度为O（dn2）。我们通过模拟和实际数据集的应用来证明这些特性。

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引用次数: 0

M-procedures robust to structural changes detection under strong mixing heavy-tailed time series models 在强混合重尾时间序列模型下，m程序对结构变化检测具有鲁棒性

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Statistical Planning and Inference

Pub Date : 2025-04-24 DOI: 10.1016/j.jspi.2025.106295

Hao Jin , Jiating Hu , Ling Zhu , Shiyu Tian , Si Zhang

Many tests of change points resort to least squares estimation method, but it can lead to bias if these observations are heavy-tailed processes. The aim of this paper is to construct a ratio-typed test based on M-estimation, which avoids the long-range variance estimation and is robust to structural change detection under strong mixing series with heavy-tailed. The proposed test consisting of M-procedures has more utility in that it allows processes in the domain of attraction of a stable law with index

κ \in (0, 2)

, not limited to

(1, 2)

. Under some regular conditions, asymptotic distribution under the null hypothesis of no change is functional of a Brownian motion, and the divergent rate under the alternative hypothesis is also provided. Furthermore, the convergence rate of a ratio-typed change point estimator is established. Simulation study illustrates there is no distortion in empirical sizes, and empirical powers have satisfactory performance. Finally, two practical applications to real examples are presented as well.

许多变化点的测试采用最小二乘估计方法，但如果这些观察是重尾过程，则可能导致偏差。本文的目的是构建一个基于m估计的比率型检验，该检验避免了长时间方差估计，并且对重尾强混合序列下的结构变化检测具有鲁棒性。所提出的由m -过程组成的检验具有更大的实用性，因为它允许在索引κ∈(0,2)的稳定定律的吸引域内的过程，而不限于（1,2）。在一定的正则条件下，无变化零假设下的渐近分布是布朗运动的泛函，并给出了备择假设下的发散率。进一步给出了比值型变点估计量的收敛速率。仿真研究表明，经验大小没有失真，经验幂具有令人满意的性能。最后，给出了两个实例的实际应用。

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引用次数: 0

Pursuing sparsity and homogeneity for multi-source high-dimensional current status data 追求多源高维现状数据的稀疏性和同质性

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Statistical Planning and Inference

Pub Date : 2025-04-23 DOI: 10.1016/j.jspi.2025.106293

Xin Ye , Yanyan Liu

Nowadays, current status data with high-dimensional predictors are prevalent in observational studies. However, for a single study, the high dimensionality and the presence of censoring pose substantial challenges to statistical analysis with limited sample size. Although integrative analysis has been widely regarded as an effective strategy to improve the estimation, the source-level heterogeneity has to be carefully addressed. In this paper, we propose an integrative analysis method for multi-source high-dimensional current status data, which can simultaneously identify the homogeneity/heterogeneity structure and select important variables. We prove that the proposed approach attains consistency in estimation, sparsity recovery, and the pursuit of homogeneity. Extensive simulation studies have been carried out to assess the finite sample performance of the proposed method. A real data analysis of multi-source ovarian cancer recurrence studies further demonstrates its practical applicability.

目前，具有高维预测因子的现状数据在观察性研究中普遍存在。然而，对于单一的研究，高维度和审查的存在对有限样本量的统计分析构成了实质性的挑战。虽然综合分析已被广泛认为是改善估计的有效策略，但必须仔细处理源级异质性。本文提出了一种多源高维电流状态数据的综合分析方法，该方法可以同时识别同质/异质结构并选择重要变量。我们证明了该方法在估计、稀疏恢复和追求同质性方面达到了一致性。已经进行了大量的仿真研究来评估所提出的方法的有限样本性能。通过对卵巢癌多源复发研究的真实数据分析，进一步证明了该方法的实用性。

引用次数: 0

Neighborhood VAR: Efficient estimation of multivariate timeseries with neighborhood information 邻域VAR：具有邻域信息的多元时间序列的有效估计

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Statistical Planning and Inference

Pub Date : 2025-03-31 DOI: 10.1016/j.jspi.2025.106277

Zhihao Hu , Shyam Ranganathan , Yang Shao , Xinwei Deng

Vector autoregression (VAR) models are popular in modeling multivariate time series in data sciences and other areas. When the number of time series is large, the number of parameters in the VAR model increases dramatically, posing great challenges for proper model estimation and inference. In this work, we propose a so-called neighborhood vector autoregression (NVAR) model to efficiently analyze large-dimensional multivariate time series. We assume that the time series have underlying neighborhood relationships, e.g., spatial or network, among them based on the inherent setting of the problem. When this neighborhood information is available or can be summarized using a distance matrix, we demonstrate that our proposed NVAR method provides a computationally efficient and theoretically sound estimation of model parameters. The performance of the proposed method is compared with other existing approaches in both simulation studies and a real-data application in environmental science.

向量自回归（VAR）模型在数据科学和其他领域的多变量时间序列建模中很受欢迎。当时间序列数量较大时，VAR模型中的参数数量会急剧增加，这对正确的模型估计和推理提出了很大的挑战。在这项工作中，我们提出了一个所谓的邻域向量自回归（NVAR）模型来有效地分析大维多元时间序列。我们假设时间序列具有潜在的邻域关系，例如，空间或网络，其中基于问题的固有设置。当邻域信息可用或可以使用距离矩阵进行汇总时，我们证明了我们提出的NVAR方法提供了计算效率高且理论上合理的模型参数估计。在模拟研究和环境科学的实际数据应用中，将该方法的性能与其他现有方法进行了比较。

引用次数: 0

Inference on linear quantile regression with dyadic data 二元数据下线性分位数回归的推理

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Statistical Planning and Inference

Pub Date : 2025-03-26 DOI: 10.1016/j.jspi.2025.106292

Hongqi Chen

This paper focuses on developing a robust inference procedure for the linear quantile regression estimator in the context of dyadic data structures. We investigate the asymptotic distribution of the quantile regression estimator under dependency structures arising from shared nodes in both undirected and directed networks. We establish consistency results for the covariance matrix estimator and provide asymptotic distributions for the associated

t

-statistic and Wald statistic, particularly in both univariate and joint hypothesis testing scenarios. To showcase the effectiveness of our proposed method, we present numerical simulations and an empirical application using international trade data. Our results demonstrate the excellent performance of the robust

t

-statistic and Wald statistic in quantile regression inference with dyadic data.

本文的重点是在二元数据结构的背景下开发一个鲁棒的线性分位数回归估计的推理程序。研究了无向网络和有向网络中由共享节点引起的依赖结构下的分位数回归估计量的渐近分布。我们建立了协方差矩阵估计量的一致性结果，并提供了相关t统计量和Wald统计量的渐近分布，特别是在单变量和联合假设检验场景中。为了证明我们提出的方法的有效性，我们给出了数值模拟和使用国际贸易数据的实证应用。结果表明，稳健t统计量和Wald统计量在二元数据的分位数回归推理中具有良好的性能。

引用次数: 0

Analysis of the rate of convergence of an over-parametrized convolutional neural network image classifier learned by gradient descent 梯度下降法学习的超参数化卷积神经网络图像分类器的收敛速度分析

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Statistical Planning and Inference

Pub Date : 2025-03-19 DOI: 10.1016/j.jspi.2025.106291

Michael Kohler , Adam Krzyżak , Benjamin Walter

Image classification based on over-parametrized convolutional neural networks with a global average-pooling layer is considered. The weights of the network are learned by gradient descent. A bound on the rate of convergence of the difference between the misclassification risk of the newly introduced convolutional neural network estimate and the minimal possible value is derived.

研究了一种基于全局平均池化层的超参数化卷积神经网络图像分类方法。网络的权值是通过梯度下降来学习的。给出了新引入的卷积神经网络估计的误分类风险与最小可能值之差的收敛速度的界。

引用次数: 0

On misspecification in cusp-type change-point models 关于尖端型变点模型的错误描述

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Statistical Planning and Inference

Pub Date : 2025-03-13 DOI: 10.1016/j.jspi.2025.106290

O.V. Chernoyarov , S. Dachian , Yu.A. Kutoyants

The problem of parameter estimation by i.i.d. observations of an inhomogeneous Poisson process is considered in situation of misspecification. The model is that of a Poissonian signal observed in presence of a homogeneous Poissonian noise. The intensity function of the process is supposed to have a cusp-type singularity at the change-point (the unknown moment of arrival of the signal), while the supposed (theoretical) and the real (observed) levels of the signal are different. The asymptotic properties of the (pseudo) MLE are described. It is shown that the estimator converges to the value minimizing the Kullback–Leibler divergence, that the normalized error of estimation converges to some limit distribution, and that its polynomial moments also converge.

研究了非齐次泊松过程在不规范情况下的参数估计问题。该模型是在均匀泊松噪声存在下观察到的泊松信号。假设过程的强度函数在变点（信号到达的未知时刻）具有尖点型奇点，而信号的假设（理论）和实际（观测）水平是不同的。描述了（伪）最大似然的渐近性质。证明了估计量收敛于使Kullback-Leibler散度最小的值，估计的归一化误差收敛于某个极限分布，其多项式矩也收敛。

引用次数: 0

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