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Least absolute deviation estimation for AR(1) processes with roots close to unity 根接近1的AR（1）过程的最小绝对偏差估计
IF 1 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2023-01-23 DOI: 10.1007/s10463-022-00864-0
Nannan Ma, Hailin Sang, Guangyu Yang
{"title":"Least absolute deviation estimation for AR(1) processes with roots close to unity","authors":"Nannan Ma,&nbsp;Hailin Sang,&nbsp;Guangyu Yang","doi":"10.1007/s10463-022-00864-0","DOIUrl":"10.1007/s10463-022-00864-0","url":null,"abstract":"<div><p>We establish the asymptotic theory of least absolute deviation estimators for AR(1) processes with autoregressive parameter satisfying <span>(n(rho _n-1)rightarrow gamma)</span> for some fixed <span>(gamma)</span> as <span>(nrightarrow infty)</span>, which is parallel to the results of ordinary least squares estimators developed by Andrews and Guggenberger (Journal of Time Series Analysis, 29, 203–212, 2008) in the case <span>(gamma = 0)</span> or Chan and Wei (Annals of Statistics, 15, 1050–1063, 1987) and Phillips (Biometrika, 74, 535–574, 1987) in the case <span>(gamma ne 0)</span>. Simulation experiments are conducted to confirm the theoretical results and to demonstrate the robustness of the least absolute deviation estimation.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":"75 5","pages":"799 - 832"},"PeriodicalIF":1.0,"publicationDate":"2023-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46897034","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
Nonparametric multiple regression by projection on non-compactly supported bases 非紧支撑基上投影的非参数多元回归
IF 1 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2023-01-22 DOI: 10.1007/s10463-022-00863-1
Florian Dussap
{"title":"Nonparametric multiple regression by projection on non-compactly supported bases","authors":"Florian Dussap","doi":"10.1007/s10463-022-00863-1","DOIUrl":"10.1007/s10463-022-00863-1","url":null,"abstract":"<div><p>We study the nonparametric regression estimation problem with a random design in <span>({mathbb{R}}^{p})</span> with <span>(pge 2)</span>. We do so by using a projection estimator obtained by least squares minimization. Our contribution is to consider non-compact estimation domains in <span>({mathbb {R}}^{p})</span>, on which we recover the function, and to provide a theoretical study of the risk of the estimator relative to a norm weighted by the distribution of the design. We propose a model selection procedure in which the model collection is random and takes into account the discrepancy between the empirical norm and the norm associated with the distribution of design. We prove that the resulting estimator automatically optimizes the bias-variance trade-off in both norms, and we illustrate the numerical performance of our procedure on simulated data.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":"75 5","pages":"731 - 771"},"PeriodicalIF":1.0,"publicationDate":"2023-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47801701","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: 4
Robust density power divergence estimates for panel data models 面板数据模型的稳健密度功率散度估计
IF 1 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2023-01-20 DOI: 10.1007/s10463-022-00862-2
Abhijit Mandal, Beste Hamiye Beyaztas, Soutir Bandyopadhyay
{"title":"Robust density power divergence estimates for panel data models","authors":"Abhijit Mandal,&nbsp;Beste Hamiye Beyaztas,&nbsp;Soutir Bandyopadhyay","doi":"10.1007/s10463-022-00862-2","DOIUrl":"10.1007/s10463-022-00862-2","url":null,"abstract":"<div><p>The panel data regression models have become one of the most widely applied statistical approaches in different fields of research, including social, behavioral, environmental sciences, and econometrics. However, traditional least-squares-based techniques frequently used for panel data models are vulnerable to the adverse effects of data contamination or outlying observations that may result in biased and inefficient estimates and misleading statistical inference. In this study, we propose a <i>minimum density power divergence</i> estimation procedure for panel data regression models with random effects to achieve robustness against outliers. The robustness, as well as the asymptotic properties of the proposed estimator, are rigorously established. The finite-sample properties of the proposed method are investigated through an extensive simulation study and an application to climate data in Oman. Our results demonstrate that the proposed estimator exhibits improved performance over some traditional and robust methods in the presence of data contamination.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":"75 5","pages":"773 - 798"},"PeriodicalIF":1.0,"publicationDate":"2023-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43954223","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
Correction to: Group least squares regression for linear models with strongly correlated predictor variables 校正:具有强相关预测变量的线性模型的组最小二乘回归
IF 1 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2023-01-11 DOI: 10.1007/s10463-022-00861-3
Min Tsao
{"title":"Correction to: Group least squares regression for linear models with strongly correlated predictor variables","authors":"Min Tsao","doi":"10.1007/s10463-022-00861-3","DOIUrl":"10.1007/s10463-022-00861-3","url":null,"abstract":"","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":"75 2","pages":"251 - 251"},"PeriodicalIF":1.0,"publicationDate":"2023-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42184841","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
A copula spectral test for pairwise time reversibility 两两时间可逆性的联结谱检验
IF 1 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2022-12-26 DOI: 10.1007/s10463-022-00859-x
Shibin Zhang
{"title":"A copula spectral test for pairwise time reversibility","authors":"Shibin Zhang","doi":"10.1007/s10463-022-00859-x","DOIUrl":"10.1007/s10463-022-00859-x","url":null,"abstract":"<div><p>In this paper, we propose a new frequency domain test for pairwise time reversibility at any specific couple of quantiles of two-dimensional marginal distribution. The proposed test is applicable to a very broad class of time series, regardless of the existence of moments and Markovian properties. By varying the couple of quantiles, the test can detect any violation of pairwise time reversibility. Our approach is based on an estimator of the <span>(L^2)</span>-distance between the imaginary part of copula spectral density kernel and its value under the null hypothesis. We show that the limiting distribution of the proposed test statistic is normal and investigate the finite sample performance by means of a simulation study. We illustrate the use of the proposed test by applying it to stock price data.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":"75 5","pages":"705 - 729"},"PeriodicalIF":1.0,"publicationDate":"2022-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44497851","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: 1
Generation of all randomizations using circuits 使用电路生成所有随机化。
IF 1 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2022-12-23 DOI: 10.1007/s10463-022-00860-4
Elena Pesce, Fabio Rapallo, Eva Riccomagno, Henry P. Wynn
{"title":"Generation of all randomizations using circuits","authors":"Elena Pesce,&nbsp;Fabio Rapallo,&nbsp;Eva Riccomagno,&nbsp;Henry P. Wynn","doi":"10.1007/s10463-022-00860-4","DOIUrl":"10.1007/s10463-022-00860-4","url":null,"abstract":"<div><p>After a rich history in medicine, randomized control trials (RCTs), both simple and complex, are in increasing use in other areas, such as web-based A/B testing and planning and design of decisions. A main objective of RCTs is to be able to measure parameters, and contrasts in particular, while guarding against biases from hidden confounders. After careful definitions of classical entities such as contrasts, an algebraic method based on circuits is introduced which gives a wide choice of randomization schemes.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":"75 4","pages":"683 - 704"},"PeriodicalIF":1.0,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10463-022-00860-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9626155","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 for semiparametric varying coefficient quantile regression models 半参数变系数分位数回归模型的模型平均
IF 1 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2022-12-22 DOI: 10.1007/s10463-022-00857-z
Zishu Zhan, Yang Li, Yuhong Yang, Cunjie Lin
{"title":"Model averaging for semiparametric varying coefficient quantile regression models","authors":"Zishu Zhan,&nbsp;Yang Li,&nbsp;Yuhong Yang,&nbsp;Cunjie Lin","doi":"10.1007/s10463-022-00857-z","DOIUrl":"10.1007/s10463-022-00857-z","url":null,"abstract":"<div><p>In this study, we propose a model averaging approach to estimating the conditional quantiles based on a set of semiparametric varying coefficient models. Different from existing literature on the subject, we consider a particular form for all candidates, where there is only one varying coefficient in each sub-model, and all the candidates under investigation may be misspecified. We propose a weight choice criterion based on a leave-more-out cross-validation objective function. Moreover, the resulting averaging estimator is more robust against model misspecification due to the weighted coefficients that adjust the relative importance of the varying and constant coefficients for the same predictors. We prove out statistical properties for each sub-model and asymptotic optimality of the weight selection method. Simulation studies show that the proposed procedure has satisfactory prediction accuracy. An analysis of a skin cutaneous melanoma data further supports the merits of the proposed approach.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":"75 4","pages":"649 - 681"},"PeriodicalIF":1.0,"publicationDate":"2022-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47825772","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: 1
Slash distributions, generalized convolutions, and extremes 斜线分布，广义卷积和极值
IF 1 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2022-12-20 DOI: 10.1007/s10463-022-00858-y
M. Arendarczyk, T. J. Kozubowski, A. K. Panorska
{"title":"Slash distributions, generalized convolutions, and extremes","authors":"M. Arendarczyk,&nbsp;T. J. Kozubowski,&nbsp;A. K. Panorska","doi":"10.1007/s10463-022-00858-y","DOIUrl":"10.1007/s10463-022-00858-y","url":null,"abstract":"<div><p>An <span>(alpha)</span>-slash distribution built upon a random variable <i>X</i> is a heavy tailed distribution corresponding to <span>(Y=X/U^{1/alpha })</span>, where <i>U</i> is standard uniform random variable, independent of <i>X</i>. We point out and explore a connection between <span>(alpha)</span>-slash distributions, which are gaining popularity in statistical practice, and generalized convolutions, which come up in the probability theory as generalizations of the standard concept of the convolution of probability measures and allow for the operation between the measures to be random itself. The stochastic interpretation of Kendall convolution discussed in this work brings this theoretical concept closer to statistical practice, and leads to new results for <span>(alpha)</span>-slash distributions connected with extremes. In particular, we show that the maximum of independent random variables with <span>(alpha)</span>-slash distributions is also a random variable with an <span>(alpha)</span>-slash distribution. Our theoretical results are illustrated by several examples involving standard and novel probability distributions and extremes.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":"75 4","pages":"593 - 617"},"PeriodicalIF":1.0,"publicationDate":"2022-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10463-022-00858-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42924932","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: 4
A unified precision matrix estimation framework via sparse column-wise inverse operator under weak sparsity 弱稀疏性下基于稀疏列逆算子的统一精度矩阵估计框架
IF 1 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2022-12-08 DOI: 10.1007/s10463-022-00856-0
Zeyu Wu, Cheng Wang, Weidong Liu
{"title":"A unified precision matrix estimation framework via sparse column-wise inverse operator under weak sparsity","authors":"Zeyu Wu,&nbsp;Cheng Wang,&nbsp;Weidong Liu","doi":"10.1007/s10463-022-00856-0","DOIUrl":"10.1007/s10463-022-00856-0","url":null,"abstract":"<div><p>In this paper, we estimate the high-dimensional precision matrix under the weak sparsity condition where many entries are nearly zero. We revisit the sparse column-wise inverse operator estimator and derive its general error bounds under the weak sparsity condition. A unified framework is established to deal with various cases including the heavy-tailed data, the non-paranormal data, and the matrix variate data. These new methods can achieve the same convergence rates as the existing methods and can be implemented efficiently.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":"75 4","pages":"619 - 648"},"PeriodicalIF":1.0,"publicationDate":"2022-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10463-022-00856-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41927406","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
Data-driven model selection for same-realization predictions in autoregressive processes 自回归过程中相同实现预测的数据驱动模型选择
IF 1 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2022-11-27 DOI: 10.1007/s10463-022-00855-1
Kare Kamila
{"title":"Data-driven model selection for same-realization predictions in autoregressive processes","authors":"Kare Kamila","doi":"10.1007/s10463-022-00855-1","DOIUrl":"10.1007/s10463-022-00855-1","url":null,"abstract":"<div><p>This paper is about the one-step ahead prediction of the future of observations drawn from an infinite-order autoregressive AR(<span>(infty )</span>) process. It aims to design penalties (fully data driven) ensuring that the selected model verifies the efficiency property but in the non-asymptotic framework. We show that the excess risk of the selected estimator enjoys the best bias-variance trade-off over the considered collection. To achieve these results, we needed to overcome the dependence difficulties by following a classical approach which consists in restricting to a set where the empirical covariance matrix is equivalent to the theoretical one. We show that this event happens with probability larger than <span>(1-c_0/n^2)</span> with <span>(c_0&gt;0)</span>. The proposed data-driven criteria are based on the minimization of the penalized criterion akin to the Mallows’s <span>(C_p)</span>.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":"75 4","pages":"567 - 592"},"PeriodicalIF":1.0,"publicationDate":"2022-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43492788","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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