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Nonlinear shrinkage test on a large‐dimensional covariance matrix 大维协方差矩阵的非线性收缩测试
IF 1.5 3区 数学
Statistica Neerlandica Pub Date : 2024-07-17 DOI: 10.1111/stan.12348
Taras Bodnar, Nestor Parolya, Frederik Veldman
{"title":"Nonlinear shrinkage test on a large‐dimensional covariance matrix","authors":"Taras Bodnar, Nestor Parolya, Frederik Veldman","doi":"10.1111/stan.12348","DOIUrl":"https://doi.org/10.1111/stan.12348","url":null,"abstract":"This paper is concerned with deriving a new test on a covariance matrix which is based on its nonlinear shrinkage estimator. The distribution of the test statistic is deduced under the null hypothesis in the large‐dimensional setting, that is, when with variables and samples both tending to infinity. The theoretical results are illustrated by means of an extensive simulation study where the new nonlinear shrinkage‐based test is compared with existing approaches, in particular with the commonly used corrected likelihood ratio test, the corrected John test, and the test based on the linear shrinkage approach. It is demonstrated that the new nonlinear shrinkage test possesses better power properties under heteroscedastic alternative.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141740615","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Estimation of a regular conditional functional by conditional U‐statistic regression 用条件 U 统计回归估计正则条件函数
IF 1.4 3区 数学
Statistica Neerlandica Pub Date : 2024-07-15 DOI: 10.1111/stan.12350
Alexis Derumigny
{"title":"Estimation of a regular conditional functional by conditional U‐statistic regression","authors":"Alexis Derumigny","doi":"10.1111/stan.12350","DOIUrl":"https://doi.org/10.1111/stan.12350","url":null,"abstract":"U‐statistics constitute a large class of estimators, generalizing the empirical mean of a random variable  to sums over every ‐tuple of distinct observations of . They may be used to estimate a regular functional of the law of . When a vector of covariates is available, a conditional U‐statistic describes the effect of on the conditional law of given , by estimating a regular conditional functional . We state nonasymptotic bounds of general conditional U‐statistics and study their asymptotics too. Assuming a parametric model of the conditional functional of interest, we propose a regression‐type estimator based on conditional U‐statistics. Its theoretical properties are derived, first in a nonasymptotic framework and then in two different asymptotic regimes. Some examples are given to illustrate our methods.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141645220","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Regression estimation using surrogate responses obtained by presmoothing 使用预平滑获得的代用响应进行回归估计
IF 1.5 3区 数学
Statistica Neerlandica Pub Date : 2024-07-11 DOI: 10.1111/stan.12351
Eni Musta, Valentin Patilea, Ingrid Van Keilegom
{"title":"Regression estimation using surrogate responses obtained by presmoothing","authors":"Eni Musta, Valentin Patilea, Ingrid Van Keilegom","doi":"10.1111/stan.12351","DOIUrl":"https://doi.org/10.1111/stan.12351","url":null,"abstract":"Presmoothing was initially introduced in the linear regression setting as a method to improve finite sample efficiency by replacing the response variable with a nonparametric estimate of the regression function. Since then, it has found success in various domains, including survival analysis. However, the use of presmoothing with multiple continuous covariates is challenging and undesirable in practice. Inspired by the cure regression setup, we derive a simple estimator for (semi)parametric models with many regressors based on 1‐dimensional presmoothing. The method is particularly valuable when the response variable is not directly observed. However, even when the response is available, presmoothing can enhance accuracy for small to moderate sample sizes. We present several applications of the proposed method in different settings and investigate its finite sample behavior through simulations.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141612644","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Hurdle GARCH models for nonnegative time series 非负时间序列的飓风 GARCH 模型
IF 1.5 3区 数学
Statistica Neerlandica Pub Date : 2024-07-11 DOI: 10.1111/stan.12349
Šárka Hudecová, Michal Pešta
{"title":"Hurdle GARCH models for nonnegative time series","authors":"Šárka Hudecová, Michal Pešta","doi":"10.1111/stan.12349","DOIUrl":"https://doi.org/10.1111/stan.12349","url":null,"abstract":"The studied semi‐continuous time series contains a nonnegligible portion of observations equal to a single value (typically zero), whereas the remaining outcomes are strictly positive. A novel class of hurdle GARCH models having dependent zero occurrences is considered and the classical maximum likelihood estimation is employed. However, a distribution of the underlying time series innovations does not belong into the exponential family, which together with the dependence of innovations makes the whole inference nonstandard. Consistency and asymptotic normality of the estimator are derived. Efficiency of the estimation is elaborated and compared with the alternative quasi‐likelihood approach. A bootstrap prediction is also discussed. An analysis of sparse nonlife insurance claims is performed.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141614987","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Endogenous and exogenous effects in self‐exciting process models of terrorist activity 恐怖活动自激过程模型中的内生和外生效应
IF 1.5 3区 数学
Statistica Neerlandica Pub Date : 2024-07-08 DOI: 10.1111/stan.12347
Fabrizio Ruggeri, Michael D. Porter, Gentry White
{"title":"Endogenous and exogenous effects in self‐exciting process models of terrorist activity","authors":"Fabrizio Ruggeri, Michael D. Porter, Gentry White","doi":"10.1111/stan.12347","DOIUrl":"https://doi.org/10.1111/stan.12347","url":null,"abstract":"A model based on the cluster process representation of the self‐exciting process model is derived to allow for variation in the excitation effects for terrorist events in a self‐exciting or cluster process model. The model's derivation and implementation details are given and applied to data from the Global Terrorism Database (National Consortium for the Study of Terrorism and Responses to Terrorism (START), 2015) from 2000 to 2013. Results regarding the practical interpretation and implications for a theoretical model paralleling existing criminological theory are discussed.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141570743","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
A note on trigonometric regression in the presence of Berkson‐type measurement error 关于存在伯克森式测量误差的三角回归的说明
IF 1.5 3区 数学
Statistica Neerlandica Pub Date : 2024-07-05 DOI: 10.1111/stan.12344
Michael T. Gorczyca, Tavish M. McDonald, Justice D. Sefas
{"title":"A note on trigonometric regression in the presence of Berkson‐type measurement error","authors":"Michael T. Gorczyca, Tavish M. McDonald, Justice D. Sefas","doi":"10.1111/stan.12344","DOIUrl":"https://doi.org/10.1111/stan.12344","url":null,"abstract":"In this note, we study how parameter vector estimation for a trigonometric regression model and the expected squared residual error computed from an estimated model are affected by Berkson‐type measurement error. Closed‐form expressions for the parameter vector and the expected squared residual error are obtained by assuming that the observed covariate data are sampled from an equispaced design and that measurement error is generated from a symmetric probability distribution with a mean of zero. Notably, these results indicate that estimates of the amplitude parameters for a trigonometric regression model suffer from attenuation bias when covariate data are mis‐measured, and that estimates of the phase‐shift parameters are unbiased.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141570880","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 for no effect in regression problems: A permutation approach 回归问题中的无效应检验：置换法
IF 1.5 3区 数学
Statistica Neerlandica Pub Date : 2024-06-21 DOI: 10.1111/stan.12346
Michał G. Ciszewski, Jakob Söhl, Ton Leenen, Bart van Trigt, Geurt Jongbloed
{"title":"Testing for no effect in regression problems: A permutation approach","authors":"Michał G. Ciszewski, Jakob Söhl, Ton Leenen, Bart van Trigt, Geurt Jongbloed","doi":"10.1111/stan.12346","DOIUrl":"https://doi.org/10.1111/stan.12346","url":null,"abstract":"Often the question arises whether can be predicted based on using a certain model. Especially for highly flexible models such as neural networks one may ask whether a seemingly good prediction is actually better than fitting pure noise or whether it has to be attributed to the flexibility of the model. This paper proposes a rigorous permutation test to assess whether the prediction is better than the prediction of pure noise. The test avoids any sample splitting and is based instead on generating new pairings of . It introduces a new formulation of the null hypothesis and rigorous justification for the test, which distinguishes it from the previous literature. The theoretical findings are applied both to simulated data and to sensor data of tennis serves in an experimental context. The simulation study underscores how the available information affects the test. It shows that the less informative the predictors, the lower the probability of rejecting the null hypothesis of fitting pure noise and emphasizes that detecting weaker dependence between variables requires a sufficient sample size.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503013","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Nonparametric causal inference with confounders missing not at random 混杂因素非随机缺失的非参数因果推断
IF 1.5 3区 数学
Statistica Neerlandica Pub Date : 2024-06-10 DOI: 10.1111/stan.12343
Jiawei Shan, Xinyu Yan
{"title":"Nonparametric causal inference with confounders missing not at random","authors":"Jiawei Shan, Xinyu Yan","doi":"10.1111/stan.12343","DOIUrl":"https://doi.org/10.1111/stan.12343","url":null,"abstract":"We consider the estimation and inference of Average Causal Effects (ACE) when confounders are missing not at random. The identification has been discussed in literature; however, limited effort has been devoted into developing feasible nonparametric inference methods. The primary challenge arises from the estimation process of the missingness mechanism, an ill‐posed problem that poses obstacles in establishing asymptotic theory. This paper contributes to filling this gap in the following ways. Firstly, we introduce a weak pseudo‐metric to guarantee a faster convergence rate of the missingness mechanism estimator. Secondly, we employ a representer to derive the explicit expression of the influence function. We also propose a practical and stable approach to estimate the variance and construct the confidence interval. We verify our theoretical results in the simulation studies.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141365642","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
A new MM algorithm for root‐finding problems 用于寻根问题的新型 MM 算法
IF 1.5 3区 数学
Statistica Neerlandica Pub Date : 2024-06-03 DOI: 10.1111/stan.12345
Xunjian Li, Shuang Li, Guo‐Liang Tian
{"title":"A new MM algorithm for root‐finding problems","authors":"Xunjian Li, Shuang Li, Guo‐Liang Tian","doi":"10.1111/stan.12345","DOIUrl":"https://doi.org/10.1111/stan.12345","url":null,"abstract":"The minorization–maximization (MM) algorithm is an optimization technique for iteratively calculating the maximizer of a concave target function rather than a root–finding tool. In this paper, we in the first time develop the MM algorithm as a new method for seeking the root of a univariate nonlinear equation . The key idea is to transfer the root–finding issue to iteratively calculate the maximizer of a concave target function by designing a new MM algorithm. According to the ascent property of the MM algorithm, we know that the proposed algorithm converges to the root and does not depend on any initial values, in contrast to Newton's method. Several statistical examples are provided to demonstrate the proposed algorithm.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141269360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
High‐dimensional sparse classification using exponential weighting with empirical hinge loss 利用指数加权和经验铰链损失进行高维稀疏分类
IF 1.5 3区 数学
Statistica Neerlandica Pub Date : 2024-05-24 DOI: 10.1111/stan.12342
The Tien Mai
{"title":"High‐dimensional sparse classification using exponential weighting with empirical hinge loss","authors":"The Tien Mai","doi":"10.1111/stan.12342","DOIUrl":"https://doi.org/10.1111/stan.12342","url":null,"abstract":"In this study, we address the problem of high‐dimensional binary classification. Our proposed solution involves employing an aggregation technique founded on exponential weights and empirical hinge loss. Through the employment of a suitable sparsity‐inducing prior distribution, we demonstrate that our method yields favorable theoretical results on prediction error. The efficiency of our procedure is achieved through the utilization of Langevin Monte Carlo, a gradient‐based sampling approach. To illustrate the effectiveness of our approach, we conduct comparisons with the logistic Lasso on simulated data and a real dataset. Our method frequently demonstrates superior performance compared to the logistic Lasso.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141150754","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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