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Uniformly asymptotic normality of estimation of the drift function for diffusion processes 扩散过程漂移函数估计的一致渐近正态性
IF 0.8 4区 数学
Journal of Statistical Planning and Inference Pub Date : 2025-02-21 DOI: 10.1016/j.jspi.2025.106274
Shanchao Yang , Qi Lan , Xueyan Xu , Zhu Liang
{"title":"Uniformly asymptotic normality of estimation of the drift function for diffusion processes","authors":"Shanchao Yang ,&nbsp;Qi Lan ,&nbsp;Xueyan Xu ,&nbsp;Zhu Liang","doi":"10.1016/j.jspi.2025.106274","DOIUrl":"10.1016/j.jspi.2025.106274","url":null,"abstract":"<div><div>The diffusion process is widely used in finance, and many scholars pay close attention to the statistical estimation of diffusion processes. Some literature has discussed the non parametric kernel estimation of drift and diffusion functions, and proved the consistency and asymptotic normality of the estimators, but the convergence rate of asymptotic normality has not been discussed yet. In this paper, we derive the convergence rate of uniformly asymptotic normality of the drift function estimator by using the method of large and small blocks for stationary and <span><math><mi>ρ</mi></math></span>-mixing diffusion process. In the case of optimal bandwidth, the rate of uniformly asymptotic normality reaches <span><math><msup><mrow><mi>n</mi></mrow><mrow><mo>−</mo><mn>2</mn><mo>/</mo><mn>15</mn></mrow></msup></math></span>. In order to prove the results, we put forward some inequalities for mixing processes with variable sampling interval, which play a key role in the study of limit theory.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"239 ","pages":"Article 106274"},"PeriodicalIF":0.8,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143579797","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Journal of Statistical Planning and Inference Pub Date : 2025-02-08 DOI: 10.1016/j.jspi.2025.106276
Daniel Gaigall , Julian Gerstenberg
{"title":"Fixed values versus empirical quantiles as thresholds in excess distribution modelling","authors":"Daniel Gaigall ,&nbsp;Julian Gerstenberg","doi":"10.1016/j.jspi.2025.106276","DOIUrl":"10.1016/j.jspi.2025.106276","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"238 ","pages":"Article 106276"},"PeriodicalIF":0.8,"publicationDate":"2025-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143379110","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Journal of Statistical Planning and Inference Pub Date : 2025-02-06 DOI: 10.1016/j.jspi.2025.106275
Jingying Zhou , Hui Jiang , Weigang Wang
{"title":"Asymptotic normality and Cramér-type moderate deviations of Yule’s nonsense correlation statistic for Ornstein–Uhlenbeck processes","authors":"Jingying Zhou ,&nbsp;Hui Jiang ,&nbsp;Weigang Wang","doi":"10.1016/j.jspi.2025.106275","DOIUrl":"10.1016/j.jspi.2025.106275","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"238 ","pages":"Article 106275"},"PeriodicalIF":0.8,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143349639","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Journal of Statistical Planning and Inference Pub Date : 2025-02-06 DOI: 10.1016/j.jspi.2025.106273
Ansgar Steland
{"title":"Detection of suspicious areas in non-stationary Gaussian fields and locally averaged non-Gaussian linear fields","authors":"Ansgar Steland","doi":"10.1016/j.jspi.2025.106273","DOIUrl":"10.1016/j.jspi.2025.106273","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"238 ","pages":"Article 106273"},"PeriodicalIF":0.8,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143349644","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Journal of Statistical Planning and Inference Pub Date : 2025-01-28 DOI: 10.1016/j.jspi.2025.106272
Riddhiman Saha , Priyam Das , Nilanjana Laha
{"title":"The two-sample location shift model under log-concavity","authors":"Riddhiman Saha ,&nbsp;Priyam Das ,&nbsp;Nilanjana Laha","doi":"10.1016/j.jspi.2025.106272","DOIUrl":"10.1016/j.jspi.2025.106272","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"238 ","pages":"Article 106272"},"PeriodicalIF":0.8,"publicationDate":"2025-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143150096","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Journal of Statistical Planning and Inference Pub Date : 2025-01-25 DOI: 10.1016/j.jspi.2025.106271
Jian Zhang , Tong Wang
{"title":"On cross-validated estimation of skew normal model","authors":"Jian Zhang ,&nbsp;Tong Wang","doi":"10.1016/j.jspi.2025.106271","DOIUrl":"10.1016/j.jspi.2025.106271","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"238 ","pages":"Article 106271"},"PeriodicalIF":0.8,"publicationDate":"2025-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143150094","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Journal of Statistical Planning and Inference Pub Date : 2025-01-06 DOI: 10.1016/j.jspi.2024.106260
Xiaoguang Wang , Rong Hu , Mengyu Li
{"title":"Model averaging prediction for survival data with time-dependent effects","authors":"Xiaoguang Wang ,&nbsp;Rong Hu ,&nbsp;Mengyu Li","doi":"10.1016/j.jspi.2024.106260","DOIUrl":"10.1016/j.jspi.2024.106260","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"238 ","pages":"Article 106260"},"PeriodicalIF":0.8,"publicationDate":"2025-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143150095","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Marginally constrained nonparametric Bayesian inference through Gaussian processes 基于高斯过程的边际约束非参数贝叶斯推理
IF 0.8 4区 数学
Journal of Statistical Planning and Inference Pub Date : 2024-12-30 DOI: 10.1016/j.jspi.2024.106261
Bingjing Tang , Vinayak Rao
{"title":"Marginally constrained nonparametric Bayesian inference through Gaussian processes","authors":"Bingjing Tang ,&nbsp;Vinayak Rao","doi":"10.1016/j.jspi.2024.106261","DOIUrl":"10.1016/j.jspi.2024.106261","url":null,"abstract":"<div><div>Nonparametric Bayesian models are used routinely as flexible and powerful models of complex data. In many situations, an applied scientist may have additional informative beliefs about the data distribution of interest, for instance, the distribution of its mean or a subset components. This often will not be compatible with the nonparametric prior. An important challenge is then to incorporate this partial prior belief into nonparametric Bayesian models. In this paper, we are motivated by settings where practitioners have additional distributional information about a subset of the coordinates of the observations being modeled. Our approach links this problem to that of conditional density modeling. Our main idea is a novel constrained Bayesian model, based on a perturbation of a parametric distribution with a transformed Gaussian process prior on the perturbation function. We develop a corresponding posterior sampling method based on data augmentation. We illustrate the efficacy of our proposed constrained nonparametric Bayesian model in a variety of real-world scenarios including modeling environmental and earthquake data.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"237 ","pages":"Article 106261"},"PeriodicalIF":0.8,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143133631","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Deterministic construction methods for asymmetrical uniform designs 不对称均匀设计的确定性构造方法
IF 0.8 4区 数学
Journal of Statistical Planning and Inference Pub Date : 2024-12-28 DOI: 10.1016/j.jspi.2024.106262
Liuping Hu , Kashinath Chatterjee , Jianhui Ning , Hong Qin
{"title":"Deterministic construction methods for asymmetrical uniform designs","authors":"Liuping Hu ,&nbsp;Kashinath Chatterjee ,&nbsp;Jianhui Ning ,&nbsp;Hong Qin","doi":"10.1016/j.jspi.2024.106262","DOIUrl":"10.1016/j.jspi.2024.106262","url":null,"abstract":"<div><div>Asymmetrical (mixed-level) uniform designs are useful for both computer and physical experiments. However, constructing these designs is often challenging due to their complex asymmetrical structure. In this paper, we propose novel methods for constructing uniform designs with mixed two-, three-, and four/nine-levels. Our construction methods are deterministic, allowing us to circumvent the complexity associated with stochastic algorithms. We evaluate uniformity using the wrap-around <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>- and Lee discrepancies. We establish useful analytic relationships between uniformity and aberration, and derive new general lower bounds for discrepancies that are tighter than those currently available in the literature. These new benchmarks can effectively measure the uniformity of asymmetrical designs. Additionally, we provide examples demonstrating the efficacy of our construction methods and the relevance of the newly obtained lower bounds. Finally, through simulations, we show that the designs produced using our methods perform well in constructing statistical surrogate models.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"237 ","pages":"Article 106262"},"PeriodicalIF":0.8,"publicationDate":"2024-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143133632","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Maximum likelihood estimation of short panel autoregressive models with flexible form of fixed effects 具有灵活形式固定效应的短面板自回归模型的最大似然估计
IF 0.8 4区 数学
Journal of Statistical Planning and Inference Pub Date : 2024-12-18 DOI: 10.1016/j.jspi.2024.106252
Kazuhiko Hayakawa, Boyan Yin
{"title":"Maximum likelihood estimation of short panel autoregressive models with flexible form of fixed effects","authors":"Kazuhiko Hayakawa,&nbsp;Boyan Yin","doi":"10.1016/j.jspi.2024.106252","DOIUrl":"10.1016/j.jspi.2024.106252","url":null,"abstract":"<div><div>This paper proposes the maximum likelihood (ML) estimator for a short panel autoregressive model with a flexible form of observed factors as well as unknown interactive fixed effects. We show that the ML estimator is consistent and asymptotically normally distributed as the number of cross-sectional units increases with the number of time periods being fixed. It should be noted that this asymptotic result holds uniformly for the autoregressive coefficient less than, equal to, or greater than one, in sharp contrast to existing estimators. Monte Carlo simulation results show that the ML estimator has desirable finite sample properties.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"237 ","pages":"Article 106252"},"PeriodicalIF":0.8,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143133630","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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