Journal of Statistical Planning and Inference最新文献

英文中文

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 : 2025-12-01 Epub 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

Asymptotic normality and Cramér-type moderate deviations of Yule’s nonsense correlation statistic for Ornstein–Uhlenbeck processes Ornstein-Uhlenbeck过程Yule无意义相关统计量的渐近正态性和cram<s:1>型中等偏差

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Statistical Planning and Inference

Pub Date : 2025-09-01 Epub Date: 2025-02-06 DOI: 10.1016/j.jspi.2025.106275

Jingying Zhou , Hui Jiang , Weigang Wang

In this paper, under discrete observations, we study the asymptotic consistency, asymptotic normality and Cramér-type moderate deviations of Yule’s nonsense correlation statistic for two Ornstein–Uhlenbeck processes. As applications, the global and local powers of the hypothesis testing for the independence between two Ornstein–Uhlenbeck processes are shown to approach one at exponential rates. Simulation experiments are conducted to confirm the theoretical results. Moreover, empirical applications illustrate the usefulness of the above mentioned statistic and the asymptotic theory. The main methods consist of the deviation inequalities and Cramér-type moderate deviations for multiple Wiener–Itô integrals and asymptotic analysis techniques.

本文在离散观测条件下，研究了两个Ornstein-Uhlenbeck过程的Yule 's无意义相关统计量的渐近一致性、渐近正态性和cram中度偏差。作为应用，证明了两个Ornstein-Uhlenbeck过程之间独立性的假设检验的全局和局部幂在指数速率下接近于1。通过仿真实验验证了理论结果。此外，实证应用说明了上述统计量和渐近理论的有效性。主要方法包括偏差不等式和多重Wiener-Itô积分的cram中度偏差和渐近分析技术。

引用次数: 0

Detection of suspicious areas in non-stationary Gaussian fields and locally averaged non-Gaussian linear fields 非平稳高斯场和局部平均非高斯线性场可疑区域的检测

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Statistical Planning and Inference

Pub Date : 2025-09-01 Epub Date: 2025-02-06 DOI: 10.1016/j.jspi.2025.106273

Ansgar Steland

Gumbel-type extreme value theory for arrays of discrete Gaussian random fields is studied and applied to some classes of discretely sampled approximately locally self-similar Gaussian processes, especially micro-noise models. Non-Gaussian discrete random fields are handled by considering the maximum of local averages of raw data or residuals. Based on some novel weak approximations with rate for (weighted) partial sums for spatial linear processes including results under a class of local alternatives, sufficient conditions for Gumbel-type asymptotics of maximum-type detection rules to detect peaks and suspicious areas in image data and, more generally, random field data, are established. The results are examined by simulations and illustrated by analyzing CT brain image data.

研究了离散高斯随机场阵列的gumbel型极值理论，并将其应用于若干类离散采样的近似局部自相似高斯过程，特别是微噪声模型。非高斯离散随机场是通过考虑原始数据局部平均值或残差的最大值来处理的。基于空间线性过程的一些新的弱近似（加权）部分和率，包括在一类局部选择下的结果，建立了最大型检测规则的gumbel型渐近性的充分条件，以检测图像数据中的峰值和可疑区域，更一般地说，是随机场数据。结果通过仿真验证，并通过分析CT脑图像数据加以说明。

引用次数: 0

On cross-validated estimation of skew normal model 斜正态模型的交叉验证估计

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Statistical Planning and Inference

Pub Date : 2025-09-01 Epub Date: 2025-01-25 DOI: 10.1016/j.jspi.2025.106271

Jian Zhang , Tong Wang

Skew normal model suffers from inferential drawbacks, namely singular Fisher information when it is close to symmetry and diverging of maximum likelihood estimation. This causes a large variation of the conventional maximum likelihood estimate. To address the above drawbacks, Azzalini and Arellano-Valle (2013) introduced maximum penalised likelihood estimation (MPLE) by subtracting a penalty function from the log-likelihood function with a pre-specified penalty coefficient. Here, we propose a cross-validated MPLE to improve its performance when the underlying model is close to symmetry. We develop a theory for MPLE, where an asymptotic rate for the cross-validated penalty coefficient is derived. We further show that the proposed cross-validated MPLE is asymptotically efficient under certain conditions. In simulation studies and a real data application, we demonstrate that the proposed estimator can outperform the conventional MPLE when the model is close to symmetry.

偏正态模型在接近对称和极大似然估计发散时存在奇异费雪信息的推理缺陷。这导致传统的最大似然估计有很大的变化。为了解决上述缺点，Azzalini和Arellano-Valle（2013）引入了最大惩罚似然估计（MPLE），通过从具有预先指定的惩罚系数的对数似然函数中减去惩罚函数。在这里，我们提出了一种交叉验证的MPLE，以提高其在底层模型接近对称时的性能。我们发展了一个MPLE理论，其中得到了交叉验证惩罚系数的渐近率。我们进一步证明了所提出的交叉验证MPLE在一定条件下是渐近有效的。在仿真研究和实际数据应用中，我们证明了该估计器在模型接近对称时优于传统的MPLE估计器。

引用次数: 0

Fixed values versus empirical quantiles as thresholds in excess distribution modelling 固定值与经验分位数作为过量分布模型的阈值

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Statistical Planning and Inference

Pub Date : 2025-09-01 Epub Date: 2025-02-08 DOI: 10.1016/j.jspi.2025.106276

Daniel Gaigall , Julian Gerstenberg

Conditional excess distribution modelling is a widely used technique, in financial and insurance mathematics or survival analysis, for instance. Classical theory considers the thresholds as fixed values. In contrast, the use of empirical quantiles as thresholds offers advantages with respect to the design of the statistical experiment. Either way, the modeller is in a non-standard situation and runs in the risk of improper usage of statistical procedures. From both points of view, statistical planning and inference, a detailed discussion is requested. For this purpose, we treat both methods and demonstrate the necessity taking into account the characteristics of the approaches in practice. In detail, we derive general statements for empirical processes related to the conditional excess distribution in both situations. As examples, estimating the mean excess and the conditional Value-at-Risk are given. We apply our findings for the testing problems of goodness-of-fit and homogeneity for the conditional excess distribution and obtain new results of outstanding interest.

条件超额分布模型是一种广泛使用的技术，例如在金融和保险数学或生存分析中。经典理论认为阈值是固定值。相比之下，使用经验分位数作为阈值在统计实验的设计方面提供了优势。无论哪种方式，建模者都处于非标准的情况下，并且存在统计程序使用不当的风险。从统计规划和推断两方面来看，都需要进行详细的讨论。为此，我们对这两种方法进行了分析，并论证了在实践中考虑到这两种方法的特点的必要性。详细地，我们推导了与两种情况下的条件过剩分布相关的经验过程的一般陈述。作为例子，给出了均值超额和条件风险值的估计。我们将我们的发现应用于检验条件过剩分布的拟合优度和均匀性问题，并获得了令人感兴趣的新结果。

引用次数: 0

The two-sample location shift model under log-concavity 对数凹性下的双样本位置移位模型

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Statistical Planning and Inference

Pub Date : 2025-09-01 Epub Date: 2025-01-28 DOI: 10.1016/j.jspi.2025.106272

Riddhiman Saha , Priyam Das , Nilanjana Laha

In this paper, we consider the two-sample location shift model, a classic semiparametric model introduced by Stein(1956). This model is known for its adaptive nature, enabling nonparametric estimation with full parametric efficiency. Existing nonparametric estimators of the location shift often depend on external tuning parameters, which restricts their practical applicability Vanet al. (1998). We demonstrate that introducing an additional assumption of log-concavity on the underlying density can alleviate the need for tuning parameters. We propose a one step estimator for location shift estimation, utilizing log-concave density estimation techniques to facilitate tuning-free estimation of the efficient influence function. While we use a truncated version of the one step estimator to theoretically demonstrate adaptivity, our simulations indicate that the one step estimators perform best with zero truncation, eliminating the need for tuning during practical implementation. Notably, the efficiency of the truncated one step estimators steadily increases as the truncation level decreases, and those with low levels of truncation exhibit nearly identical empirical performance to the estimator with zero truncation. We apply our method to investigate the location shift in the distribution of Spanish annual household incomes following the 2008 financial crisis.

本文考虑Stein（1956）提出的经典半参数模型——双样本位置移位模型。该模型以其自适应特性而闻名，使非参数估计具有充分的参数效率。现有的位置移位的非参数估计往往依赖于外部调谐参数，这限制了它们的实际适用性（Vanet al., 1998）。我们证明了在底层密度上引入一个额外的对数凹性假设可以减轻对参数调优的需要。我们提出了一种单步估计器用于位置移位估计，利用对数凹密度估计技术来促进有效影响函数的无调谐估计。虽然我们使用截断版本的一步估计器来从理论上证明自适应性，但我们的模拟表明，一步估计器在零截断时表现最佳，从而消除了在实际实现期间调优的需要。值得注意的是，截断的一步估计器的效率随着截断水平的降低而稳步提高，并且截断水平低的估计器与零截断的估计器表现出几乎相同的经验性能。我们运用我们的方法来调查2008年金融危机后西班牙家庭年收入分布的区位转移。

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引用次数: 0

Model averaging prediction for survival data with time-dependent effects 具有时间依赖效应的生存数据的模型平均预测

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Statistical Planning and Inference

Pub Date : 2025-09-01 Epub Date: 2025-01-06 DOI: 10.1016/j.jspi.2024.106260

Xiaoguang Wang , Rong Hu , Mengyu Li

It is a fundamental task to predict patients’ survival outcomes in clinical research. As an extension of the Cox proportional hazards model, the time-dependent coefficient Cox model is typically utilized for time-to-event data with time-dependent effects. When the number of covariates is large, the curse of dimensionality emerges for most existing methods. To overcome the limitation and improve predictive performance, a semiparametric model averaging approach is proposed for the time-dependent coefficient Cox model. We introduce a novel criterion to estimate model weights and demonstrate its theoretical properties. Extensive simulation studies are conducted to compare the proposed technique with existing competitive methods. A real clinical data set is also analyzed to illustrate the advantages of our approach.

预测患者的生存结局是临床研究的一项基本任务。作为Cox比例风险模型的扩展，时间依赖系数Cox模型通常用于具有时间依赖效应的时间-事件数据。当协变量数量较大时，大多数现有方法都会出现维数问题。为了克服时间依赖系数Cox模型的局限性，提高预测性能，提出了一种半参数模型平均方法。我们引入了一种新的估计模型权重的准则，并证明了它的理论性质。进行了广泛的仿真研究，以比较所提出的技术与现有的竞争方法。一个真实的临床数据集也被分析来说明我们的方法的优点。

引用次数: 0

Nonparametric estimators of inequality curves and inequality measures 不等式曲线的非参数估计和不等式测度

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Statistical Planning and Inference

Pub Date : 2025-07-01 Epub Date: 2024-11-28 DOI: 10.1016/j.jspi.2024.106251

Alicja Jokiel-Rokita, Sylwester Pia̧tek

Classical inequality curves and inequality measures are defined for distributions with finite mean value. Moreover, their empirical counterparts are not resistant to outliers. For these reasons, quantile versions of known inequality curves such as the Lorenz, Bonferroni, Zenga and

D

curves, and quantile versions of inequality measures such as the Gini, Bonferroni, Zenga and

D

indices have been proposed in the literature. We propose various nonparametric estimators of quantile versions of inequality curves and inequality measures, prove their consistency, and compare their accuracy in a simulation study. We also give examples of the use of quantile versions of inequality measures in real data analysis.

经典的不等式曲线和不等式测度是针对有限均值分布定义的。此外，他们的经验对应物对异常值没有抵抗力。由于这些原因，文献中已经提出了已知不平等曲线的分位数版本，如Lorenz， Bonferroni， Zenga和D曲线，以及不平等测量的分位数版本，如基尼指数，Bonferroni指数，Zenga指数和D指数。我们提出了不等式曲线和不等式测度的分位数版本的各种非参数估计，证明了它们的一致性，并在模拟研究中比较了它们的准确性。我们还给出了在实际数据分析中使用分位数版本的不平等度量的例子。

引用次数: 0

Modeling and testing for endpoint-inflated count time series with bounded support 有界支持端点膨胀计数时间序列的建模与测试

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Statistical Planning and Inference

Pub Date : 2025-07-01 Epub Date: 2024-11-15 DOI: 10.1016/j.jspi.2024.106248

Yao Kang , Xiaojing Fan , Jie Zhang , Ying Tang

Count time series with bounded support frequently exhibit binomial overdispersion, zero inflation and right-endpoint inflation in practical scenarios. Numerous models have been proposed for the analysis of bounded count time series with binomial overdispersion and zero inflation, yet right-endpoint inflation has received comparatively less attention. To better capture these features, this article introduces three versions of extended first-order binomial autoregressive (BAR(1)) models with endpoint inflation. Corresponding stochastic properties of the new models are investigated and model parameters are estimated by the conditional maximum likelihood and quasi-maximum likelihood methods. A binomial right-endpoint inflation index is also constructed and further used to test whether the data set has endpoint-inflated characteristic with respect to a BAR(1) process. Finally, the proposed models are applied to two real data examples. Firstly, we illustrate the usefulness of the proposed models through an application to the voting data on supporting interest rate changes during consecutive monthly meetings of the Monetary Policy Council at the National Bank of Poland. Then, we apply the proposed models to the number of police stations that received at least one drunk driving report per month. The results of the two real data examples indicate that the new models have significant advantages in terms of fitting performance for the bounded count time series with endpoint inflation.

具有有界支持的计数时间序列在实际场景中经常表现为二项过分散、零膨胀和右端点膨胀。对于具有二项过分散和零膨胀的有界计数时间序列的分析，已经提出了许多模型，但右端点膨胀受到的关注相对较少。为了更好地捕捉这些特征，本文介绍了具有端点膨胀的扩展一阶二项自回归（BAR(1)）模型的三个版本。研究了新模型的随机性质，并利用条件极大似然和拟极大似然方法估计了模型参数。还构造了一个二项式右端点膨胀指数，并进一步用于测试数据集相对于BAR(1)过程是否具有端点膨胀特征。最后，将所提出的模型应用于两个实际数据实例。首先，我们通过对波兰国家银行货币政策委员会连续每月会议期间支持利率变化的投票数据的应用来说明所提出模型的实用性。然后，我们将所提出的模型应用于每月至少收到一份酒驾报告的警察局数量。两个实际数据示例的结果表明，新模型在具有端点膨胀的有界计数时间序列的拟合性能方面具有显著的优势。

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引用次数: 0

Sieve estimation of the accelerated mean model based on panel count data 基于面板计数数据的加速平均模型的筛分估计

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Statistical Planning and Inference

Pub Date : 2025-07-01 Epub Date: 2024-11-12 DOI: 10.1016/j.jspi.2024.106247

Xiaoyang Li , Zhi-Sheng Ye , Xingqiu Zhao

Panel count data are gathered when subjects are examined at discrete times during a study, and only the number of recurrent events occurring before each examination time is recorded. We consider a semiparametric accelerated mean model for panel count data in which the effect of the covariates is to transform the time scale of the baseline mean function. Semiparametric inference for the model is inherently challenging because the finite-dimensional regression parameters appear in the argument of the (infinite-dimensional) functional parameter, i.e., the baseline mean function, leading to the phenomenon of bundled parameters. We propose sieve pseudolikelihood and likelihood methods to construct the random criterion function for estimating the model parameters. An inexact block coordinate ascent algorithm is used to obtain these estimators. We establish the consistency and rate of convergence of the proposed estimators, as well as the asymptotic normality of the estimators of the regression parameters. Novel consistent estimators of the asymptotic covariances of the estimated regression parameters are derived by leveraging the counting process associated with the examination times. Comprehensive simulation studies demonstrate that the optimization algorithm is much less sensitive to the initial values than the Newton–Raphson method. The proposed estimators perform well for practical sample sizes, and are more efficient than existing methods. An example based on real data shows that due to this efficiency gain, the proposed method is better able to detect the significance of practically meaningful covariates than an existing method.

面板计数数据是在研究过程中对受试者进行离散时间检查时收集的数据，只记录每次检查时间之前发生的重复事件的数量。我们考虑了面板计数数据的半参数加速均值模型，其中协变量的作用是转换基线均值函数的时间尺度。由于有限维回归参数出现在（无限维）函数参数（即基线均值函数）的参数中，导致了捆绑参数现象，因此该模型的半参数推断本身就具有挑战性。我们提出了筛分伪似然法和似然法，以构建估计模型参数的随机准则函数。我们使用非精确块坐标上升算法来获得这些估计值。我们确定了所提出的估计值的一致性和收敛率，以及回归参数估计值的渐近正态性。通过利用与考试时间相关的计数过程，我们得出了估计回归参数渐近协方差的新一致估计值。综合模拟研究表明，优化算法对初始值的敏感度远低于牛顿-拉斐森方法。所提出的估计方法在实际样本量中表现良好，比现有方法更有效。一个基于真实数据的例子表明，由于效率的提高，所提出的方法比现有方法更能检测出具有实际意义的协变量的重要性。

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