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Tuning parameter selection for the adaptive nuclear norm regularized trace regression 自适应核范数正则化轨迹回归的参数选择
IF 0.8 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2025-03-27 DOI: 10.1007/s10463-025-00926-z
Yiting Ma, Pan Shang, Lingchen Kong
{"title":"Tuning parameter selection for the adaptive nuclear norm regularized trace regression","authors":"Yiting Ma,&nbsp;Pan Shang,&nbsp;Lingchen Kong","doi":"10.1007/s10463-025-00926-z","DOIUrl":"10.1007/s10463-025-00926-z","url":null,"abstract":"<div><p>Regularized models have been applied in lots of areas in recent years, with high dimensional data sets being popular. Because that tuning parameter decides the theoretical performance and computational efficiency of the regularized models, tuning parameter selection is a basic and important issue. We consider the tuning parameter selection for adaptive nuclear norm regularized trace regression, which achieves by the Bayesian information criterion (BIC). The proposed BIC is established with the help of an unbiased estimator of degrees of freedom. Under some regularized conditions, this BIC is proved to achieve the rank consistency of the tuning parameter selection. That is the model solution under selected tuning parameter converges to the true solution and has the same rank with that of the true solution in probability. Some numerical results are presented to evaluate the performance of the proposed BIC on tuning parameter selection.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":"77 3","pages":"491 - 516"},"PeriodicalIF":0.8,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143879626","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 uniform consistency of nonparametric estimators smoothed by the gamma kernel 核光滑非参数估计量的一致相合性
IF 0.8 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2025-02-17 DOI: 10.1007/s10463-024-00923-8
Benedikt Funke, Masayuki Hirukawa
{"title":"On uniform consistency of nonparametric estimators smoothed by the gamma kernel","authors":"Benedikt Funke,&nbsp;Masayuki Hirukawa","doi":"10.1007/s10463-024-00923-8","DOIUrl":"10.1007/s10463-024-00923-8","url":null,"abstract":"<div><p>This paper documents a set of uniform consistency results with rates for nonparametric density and regression estimators smoothed by the gamma kernel having support on the nonnegative real line. It is known that this kernel can well calibrate the shapes of ‘cost’ distributions that are characterized by a sharp peak in the vicinity of the origin and a long right tail. In this paper, weak and strong uniform consistency and corresponding convergence rates of gamma kernel estimators are explored in a multivariate framework. Our analysis is built on compact sets expanding to the nonnegative orthant and general sequences of smoothing parameters. The results are useful for asymptotic analysis of two-step semiparametric estimation using a first-step kernel estimate as a plug-in.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":"77 3","pages":"459 - 489"},"PeriodicalIF":0.8,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143879616","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
Semiparametric transformation models for survival data with dependent censoring 具有相关删减的生存数据半参数变换模型
IF 0.8 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2024-12-26 DOI: 10.1007/s10463-024-00921-w
Negera Wakgari Deresa, Ingrid Van Keilegom
{"title":"Semiparametric transformation models for survival data with dependent censoring","authors":"Negera Wakgari Deresa,&nbsp;Ingrid Van Keilegom","doi":"10.1007/s10463-024-00921-w","DOIUrl":"10.1007/s10463-024-00921-w","url":null,"abstract":"<div><p>This paper proposes copula based semiparametric transformation models to take dependent censoring into account. The model is based on a parametric Archimedean copula model for the relation between the survival time (<span>(T_1)</span>) and the censoring time (<span>(T_2)</span>), whereas the marginal distributions of <span>(T_1)</span> and <span>(T_2)</span> follow a semiparametric transformation model. We show that this flexible model is identified based on the distribution of the observable variables, and propose estimators of the nonparametric functions and the finite dimensional parameters. An estimation algorithm is provided for implementing the new method. We establish the asymptotic properties of the estimators of the model parameters and the nonparametric functions. The theoretical development can serve as a valuable template when dealing with estimating equations that involve systems of linear differential equations. We also investigate the performance of the proposed method using finite sample simulations and real data example.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":"77 3","pages":"425 - 457"},"PeriodicalIF":0.8,"publicationDate":"2024-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143879581","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
Robust and efficient parameter estimation for discretely observed stochastic processes 离散观测随机过程的鲁棒有效参数估计
IF 0.8 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2024-12-23 DOI: 10.1007/s10463-024-00922-9
Rohan Hore, Abhik Ghosh
{"title":"Robust and efficient parameter estimation for discretely observed stochastic processes","authors":"Rohan Hore,&nbsp;Abhik Ghosh","doi":"10.1007/s10463-024-00922-9","DOIUrl":"10.1007/s10463-024-00922-9","url":null,"abstract":"<div><p>In various practical situations, we encounter data from stochastic processes which can be efficiently modeled by an appropriate parametric model for subsequent statistical analyses. Unfortunately, maximum likelihood (ML) estimation, the most common approach, is sensitive to slight model deviations or data contamination due to its well-known lack of robustness. Since the non-parametric alternatives often sacrifice efficiency, in this paper we develop a robust parameter estimation procedure for discretely observed data from a parametric stochastic process model which exploits the nice properties of the popular density power divergence measure. In particular, here we define the minimum density power divergence estimators (MDPDE) for the independent increment and the Markov processes. We establish the asymptotic consistency and distributional results for the proposed MDPDEs in these dependent stochastic process setups and illustrate their benefits over the usual ML estimator for common examples like the Poisson process, drifted Brownian motion and the auto-regressive models.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":"77 3","pages":"387 - 424"},"PeriodicalIF":0.8,"publicationDate":"2024-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143879584","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
Confidence bounds for the true discovery proportion based on the exact distribution of the number of rejections 真实发现比例的置信限基于拒绝数量的精确分布
IF 0.8 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2024-12-13 DOI: 10.1007/s10463-024-00920-x
Friederike Preusse, Anna Vesely, Thorsten Dickhaus
{"title":"Confidence bounds for the true discovery proportion based on the exact distribution of the number of rejections","authors":"Friederike Preusse,&nbsp;Anna Vesely,&nbsp;Thorsten Dickhaus","doi":"10.1007/s10463-024-00920-x","DOIUrl":"10.1007/s10463-024-00920-x","url":null,"abstract":"<div><p>In multiple hypotheses testing it has become widely popular to make inference on the true discovery proportion (TDP) of a set <span>(mathscr {M})</span> of null hypotheses. This approach is useful for several application fields, such as neuroimaging and genomics. Several procedures to compute simultaneous lower confidence bounds for the TDP have been suggested in prior literature. Simultaneity allows for post-hoc selection of <span>(mathscr {M})</span>. If sets of interest are specified a priori, it is possible to gain power by removing the simultaneity requirement. We present an approach to compute lower confidence bounds for the TDP if the set of null hypotheses is defined a priori. The proposed method determines the bounds using the exact distribution of the number of rejections based on a step-up multiple testing procedure under independence assumptions. We assess robustness properties of our procedure and apply it to real data from the field of functional magnetic resonance imaging.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":"77 2","pages":"191 - 216"},"PeriodicalIF":0.8,"publicationDate":"2024-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143513289","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
Testing overidentifying restrictions on high-dimensional instruments and covariates 测试高维工具和协变量的过度识别限制
IF 0.8 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2024-12-05 DOI: 10.1007/s10463-024-00918-5
Hongwei Shi, Xinyu Zhang, Xu Guo, Baihua He, Chenyang Wang
{"title":"Testing overidentifying restrictions on high-dimensional instruments and covariates","authors":"Hongwei Shi,&nbsp;Xinyu Zhang,&nbsp;Xu Guo,&nbsp;Baihua He,&nbsp;Chenyang Wang","doi":"10.1007/s10463-024-00918-5","DOIUrl":"10.1007/s10463-024-00918-5","url":null,"abstract":"<div><p>The validity of instruments plays a crucial role in addressing endogenous treatment effects and instruments that violate the exclusion restriction are invalid. This paper concerns the overidentifying restrictions test for evaluating the validity of instruments in the high-dimensional instrumental variable model. We confront the challenge of high dimensionality by introducing a new testing procedure based on <i>U</i>-statistic. Our procedure allows the number of instruments and covariates to be in exponential order of the sample size. Under some mild conditions, we establish the asymptotic normality of the proposed test statistic under the null and local alternative hypotheses. The effectiveness of the proposed method is clearly supported by simulations and its application to a real dataset on trade and economic growth.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":"77 2","pages":"331 - 352"},"PeriodicalIF":0.8,"publicationDate":"2024-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143513249","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
Comparison and equality of generalized (psi )-estimators 广义(psi ) -估计量的比较与等价
IF 0.8 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2024-12-04 DOI: 10.1007/s10463-024-00916-7
Mátyás Barczy, Zsolt Páles
{"title":"Comparison and equality of generalized (psi )-estimators","authors":"Mátyás Barczy,&nbsp;Zsolt Páles","doi":"10.1007/s10463-024-00916-7","DOIUrl":"10.1007/s10463-024-00916-7","url":null,"abstract":"<div><p>We solve the comparison problem for generalized <span>(psi )</span>-estimators introduced by Barczy and Páles (<i>arXiv</i>: 2211.06026, 2022). Namely, we derive several necessary and sufficient conditions under which a generalized <span>(psi )</span>-estimator less than or equal to another <span>(psi )</span>-estimator for any sample. We also solve the corresponding equality problem for generalized <span>(psi )</span>-estimators. We also apply our results for some known statistical estimators such as for empirical expectiles and Mathieu-type estimators and for solutions of likelihood equations in case of normal, a Beta-type, Gamma, Lomax (Pareto type II), lognormal and Laplace distributions.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":"77 2","pages":"217 - 250"},"PeriodicalIF":0.8,"publicationDate":"2024-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143513149","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
Large-sample properties of multiple imputation estimators for parameters of logistic regression with covariates missing at random separately or simultaneously 单独或同时随机缺失协变量的逻辑回归参数的多重估计量的大样本性质
IF 0.8 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2024-12-02 DOI: 10.1007/s10463-024-00914-9
Phuoc-Loc Tran, Shen-Ming Lee, Truong-Nhat Le, Chin-Shang Li
{"title":"Large-sample properties of multiple imputation estimators for parameters of logistic regression with covariates missing at random separately or simultaneously","authors":"Phuoc-Loc Tran,&nbsp;Shen-Ming Lee,&nbsp;Truong-Nhat Le,&nbsp;Chin-Shang Li","doi":"10.1007/s10463-024-00914-9","DOIUrl":"10.1007/s10463-024-00914-9","url":null,"abstract":"<div><p>We examine the asymptotic properties of two multiple imputation (MI) estimators, given in the study of Lee et al. (<u>Computational Statistics</u>, <b>38</b>, 899–934, 2023) for the parameters of logistic regression with both sets of discrete or categorical covariates that are missing at random separately or simultaneously. The proposed estimated asymptotic variances of the two MI estimators address a limitation observed with Rubin’s estimated variances, which lead to underestimate the variances of the two MI estimators (Rubin, 1987, <u>Statistical Analysis with Missing Data</u>, New York:Wiley). Simulation results demonstrate that our two proposed MI methods outperform the complete-case, semiparametric inverse probability weighting, random forest MI using chained equations, and stochastic approximation of expectation-maximization methods. To illustrate the methodology’s practical application, we provide a real data example from a survey conducted at the Feng Chia night market in Taichung City, Taiwan.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":"77 2","pages":"251 - 287"},"PeriodicalIF":0.8,"publicationDate":"2024-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143513126","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
Random mixture Cox point processes 随机混合Cox点过程
IF 0.8 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2024-11-22 DOI: 10.1007/s10463-024-00915-8
A. C. Micheas
{"title":"Random mixture Cox point processes","authors":"A. C. Micheas","doi":"10.1007/s10463-024-00915-8","DOIUrl":"10.1007/s10463-024-00915-8","url":null,"abstract":"<div><p>We introduce and study a new class of Cox point processes, based on random mixture models of exponential family components for the intensity function of the underlying Poisson process. We investigate theoretical properties of the proposed probability distributions of the point process, as well as provide procedures for parameter estimation using a classical and Bayesian approach. We illustrate the richness of the new models through examples, simulations and real data applications.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":"77 2","pages":"289 - 330"},"PeriodicalIF":0.8,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143513303","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
Non-explicit formula of boundary crossing probabilities by the Girsanov theorem 用格萨诺夫定理求边界穿越概率的非显式公式
IF 0.8 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2024-11-05 DOI: 10.1007/s10463-024-00917-6
Yoann Potiron
{"title":"Non-explicit formula of boundary crossing probabilities by the Girsanov theorem","authors":"Yoann Potiron","doi":"10.1007/s10463-024-00917-6","DOIUrl":"10.1007/s10463-024-00917-6","url":null,"abstract":"<div><p>This paper derives several formulae for the probability that a Wiener process, which has a stochastic drift and random variance, crosses a one-sided stochastic boundary within a finite time interval. A non-explicit formula is first obtained by the Girsanov theorem when considering an equivalent probability measure in which the boundary is constant and equal to its starting value. A more explicit formula is then achieved by decomposing the Radon–Nikodym derivative inverse. This decomposition expresses it as the product of a random variable, which is measurable with respect to the Wiener process’s final value, and an independent random variable. We also provide an explicit formula based on a strong theoretical assumption. To apply the Girsanov theorem, we assume that the difference between the drift increment and the boundary increment, divided by the standard deviation, is absolutely continuous. Additionally, we assume that its derivative satisfies Novikov’s condition.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":"77 3","pages":"353 - 385"},"PeriodicalIF":0.8,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143879622","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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