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Estimation of value-at-risk by $$L^{p}$$ quantile regression 用 $$L^{p}$$ 量化回归估算风险价值
IF 1 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2024-09-19 DOI: 10.1007/s10463-024-00911-y
Peng Sun, Fuming Lin, Haiyang Xu, Kaizhi Yu
{"title":"Estimation of value-at-risk by $$L^{p}$$ quantile regression","authors":"Peng Sun, Fuming Lin, Haiyang Xu, Kaizhi Yu","doi":"10.1007/s10463-024-00911-y","DOIUrl":"https://doi.org/10.1007/s10463-024-00911-y","url":null,"abstract":"<p>Exploring more accurate estimates of financial value at risk (VaR) has always been an important issue in applied statistics. To this end either quantile or expectile regression methods are widely employed at present, but an accumulating body of research indicates that <span>(L^{p})</span> quantile regression outweighs both quantile and expectile regression in many aspects. In view of this, the paper extends <span>(L^{p})</span> quantile regression to a general classical nonlinear conditional autoregressive model and proposes a new model called the conditional <span>(L^{p})</span> quantile nonlinear autoregressive regression model (CAR-<span>(L^{p})</span>-quantile model for short). Limit theorems for regression estimators are proved in mild conditions, and algorithms are provided for obtaining parameter estimates and the optimal value of <i>p</i>. Simulation study of estimation’s quality is given. Then, a CLVaR method calculating VaR based on the CAR-<span>(L^{p})</span>-quantile model is elaborated. Finally, a real data analysis is conducted to illustrate virtues of our proposed methods.</p>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142254402","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
Simplified quasi-likelihood analysis for a locally asymptotically quadratic random field 局部渐近二次随机场的简化准概率分析
IF 1 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2024-09-14 DOI: 10.1007/s10463-024-00907-8
Nakahiro Yoshida
{"title":"Simplified quasi-likelihood analysis for a locally asymptotically quadratic random field","authors":"Nakahiro Yoshida","doi":"10.1007/s10463-024-00907-8","DOIUrl":"https://doi.org/10.1007/s10463-024-00907-8","url":null,"abstract":"<p>The IHK program is a general framework in asymptotic decision theory, introduced by Ibragimov and Hasminskii and extended to semimartingales by Kutoyants. The quasi-likelihood analysis (QLA) asserts that a polynomial type large deviation inequality is always valid if the quasi-likelihood random field is asymptotically quadratic and if a key index reflecting the identifiability is non-degenerate. As a result, following the IHK program, the QLA gives a way to inference for various nonlinear stochastic processes. This paper provides a reformed and simplified version of the QLA and improves accessibility to the theory. As an example of the advantages of the scheme, the user can obtain asymptotic properties of the quasi-Bayesian estimator by only verifying non-degeneracy of the key index.</p>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142254403","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
Asymptotic expected sensitivity function and its applications to measures of monotone association 渐近预期灵敏度函数及其在单调关联测量中的应用
IF 0.8 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2024-08-17 DOI: 10.1007/s10463-024-00910-z
Qingyang Zhang
{"title":"Asymptotic expected sensitivity function and its applications to measures of monotone association","authors":"Qingyang Zhang","doi":"10.1007/s10463-024-00910-z","DOIUrl":"10.1007/s10463-024-00910-z","url":null,"abstract":"<div><p>We introduce a new type of influence function, the asymptotic expected sensitivity function, which is often equivalent to but mathematically more tractable than the traditional one based on the Gâteaux derivative. To illustrate, we study the robustness of some important measures of association, including Spearman’s rank correlation and Kendall’s concordance measure, and the recently developed Chatterjee’s correlation.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142199920","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
Penalized estimation for non-identifiable models 不可识别模式的惩罚性估计
IF 0.8 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2024-08-01 DOI: 10.1007/s10463-024-00905-w
Junichiro Yoshida, Nakahiro Yoshida
{"title":"Penalized estimation for non-identifiable models","authors":"Junichiro Yoshida,&nbsp;Nakahiro Yoshida","doi":"10.1007/s10463-024-00905-w","DOIUrl":"10.1007/s10463-024-00905-w","url":null,"abstract":"<div><p>We derive asymptotic properties of penalized estimators for singular models for which identifiability may break and the true parameter values can lie on the boundary of the parameter space. Selection consistency of the estimators is also validated. The problem that the true values lie on the boundary is solved by our previous results applicable to singular models, besides, penalized estimation and non-ergodic statistics. To overcome non-identifiability, we consider a suitable penalty such as the non-convex Bridge and the adaptive Lasso that stabilize the asymptotic behavior of the estimator and shrink inactive parameters. Then the estimator converges to one of the most parsimonious values among all the true values. The oracle property can also be obtained even if likelihood ratio tests for model selection are labor intensive due to singularity of models. Examples are: a superposition of parametric proportional hazard models and a counting process having intensity with multicollinear covariates.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141871728","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
Hidden AR process and adaptive Kalman filter 隐藏的 AR 过程和自适应卡尔曼滤波器
IF 1 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2024-07-25 DOI: 10.1007/s10463-024-00908-7
Yury A. Kutoyants
{"title":"Hidden AR process and adaptive Kalman filter","authors":"Yury A. Kutoyants","doi":"10.1007/s10463-024-00908-7","DOIUrl":"https://doi.org/10.1007/s10463-024-00908-7","url":null,"abstract":"<p>This work discusses a model of a partially observed linear system that depends on some unknown parameters. An approximation of the unobserved component is proposed, which involves three steps. First, a method of moment estimator of unknown parameters is constructed, and second, this estimator is used to define the one-step MLE-process. Finally, the last estimator is substituted into the equations of the Kalman filter. The solution of obtained equations provides us with the desired approximation (adaptive Kalman filter). The asymptotic properties of all the mentioned estimators and both maximum likelihood and Bayesian estimators of the unknown parameters are detailed. The asymptotic efficiency of adaptive filtering is discussed.</p>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141774532","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
Minimizing robust density power-based divergences for general parametric density models 最小化一般参数密度模型的稳健密度幂基发散
IF 0.8 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2024-05-02 DOI: 10.1007/s10463-024-00906-9
Akifumi Okuno
{"title":"Minimizing robust density power-based divergences for general parametric density models","authors":"Akifumi Okuno","doi":"10.1007/s10463-024-00906-9","DOIUrl":"10.1007/s10463-024-00906-9","url":null,"abstract":"<div><p>Density power divergence (DPD) is designed to robustly estimate the underlying distribution of observations, in the presence of outliers. However, DPD involves an integral of the power of the parametric density models to be estimated; the explicit form of the integral term can be derived only for specific densities, such as normal and exponential densities. While we may perform a numerical integration for each iteration of the optimization algorithms, the computational complexity has hindered the practical application of DPD-based estimation to more general parametric densities. To address the issue, this study introduces a stochastic approach to minimize DPD for general parametric density models. The proposed approach can also be employed to minimize other density power-based <span>(gamma)</span>-divergences, by leveraging unnormalized models. We provide <span>R</span> package for implementation of the proposed approach in https://github.com/oknakfm/sgdpd.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140888409","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
Empirical likelihood MLE for joint modeling right censored survival data with longitudinal covariates 对带有纵向协变量的右删失生存数据进行联合建模的经验似然 MLE
IF 0.8 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2024-04-29 DOI: 10.1007/s10463-024-00899-5
Jian-Jian Ren, Yuyin Shi
{"title":"Empirical likelihood MLE for joint modeling right censored survival data with longitudinal covariates","authors":"Jian-Jian Ren,&nbsp;Yuyin Shi","doi":"10.1007/s10463-024-00899-5","DOIUrl":"10.1007/s10463-024-00899-5","url":null,"abstract":"<div><p>Up to now, almost all existing methods for joint modeling survival data and longitudinal data rely on parametric/semiparametric assumptions on longitudinal covariate process, and the resulting inferences critically depend on the validity of these assumptions that are difficult to verify in practice. The kernel method-based procedures rely on choices of kernel function and bandwidth, and none of the existing methods provides estimate for the baseline distribution in proportional hazards model. This article proposes a proportional hazards model for joint modeling right censored survival data and intensive longitudinal data taking into account of within-subject historic change patterns. Without any parametric/semiparametric assumptions or use of kernel method, we derive empirical likelihood-based maximum likelihood estimators and partial likelihood estimators for the regression parameter and the baseline distribution function. We develop stable computing algorithms and present some simulation results. Analyses of real dataset are conducted for smoking cessation data and liver disease data.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140826716","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
Assessing the coverage probabilities of fixed-margin confidence intervals for the tail conditional allocation 评估尾部条件分配的固定边际置信区间的覆盖概率
IF 0.8 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2024-04-23 DOI: 10.1007/s10463-024-00904-x
N. V. Gribkova, J. Su, R. Zitikis
{"title":"Assessing the coverage probabilities of fixed-margin confidence intervals for the tail conditional allocation","authors":"N. V. Gribkova,&nbsp;J. Su,&nbsp;R. Zitikis","doi":"10.1007/s10463-024-00904-x","DOIUrl":"10.1007/s10463-024-00904-x","url":null,"abstract":"<div><p>The tail conditional allocation plays an important role in a number of areas, including economics, finance, insurance, and management. Fixed-margin confidence intervals and the assessment of their coverage probabilities are of much interest. In this paper, we offer a convenient way to achieve these goals via resampling. The theoretical part of the paper, which is technically demanding, is rigorously established under minimal conditions to facilitate the widest practical use. A simulation-based study and an analysis of real data illustrate the performance of the developed methodology.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140798164","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
Quasi-maximum likelihood estimation and penalized estimation under non-standard conditions 非标准条件下的准极大似然估计和惩罚性估计
IF 0.8 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2024-04-23 DOI: 10.1007/s10463-024-00901-0
Junichiro Yoshida, Nakahiro Yoshida
{"title":"Quasi-maximum likelihood estimation and penalized estimation under non-standard conditions","authors":"Junichiro Yoshida,&nbsp;Nakahiro Yoshida","doi":"10.1007/s10463-024-00901-0","DOIUrl":"10.1007/s10463-024-00901-0","url":null,"abstract":"<div><p>The purpose of this article is to develop a general parametric estimation theory that allows the derivation of the limit distribution of estimators in non-regular models where the true parameter value may lie on the boundary of the parameter space or where even identifiability fails. For that, we propose a more general local approximation of the parameter space (at the true value) than previous studies. This estimation theory is comprehensive in that it can handle penalized estimation as well as quasi-maximum likelihood estimation (in the ergodic or non-ergodic statistics) under such non-regular models. In penalized estimation, depending on the boundary constraint, even the concave Bridge estimator does not necessarily give selection consistency. Therefore, we describe some sufficient condition for selection consistency, precisely evaluating the balance between the boundary constraint and the form of the penalty. An example is penalized MLE of variance components of random effects in linear mixed models.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140798165","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 delineation of new classes of exponential dispersion models supported on the set of nonnegative integers 非负整数集支持的指数离散模型新类别划分
IF 0.8 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2024-04-22 DOI: 10.1007/s10463-024-00903-y
Shaul K. Bar-Lev, Gérard Letac, Ad Ridder
{"title":"A delineation of new classes of exponential dispersion models supported on the set of nonnegative integers","authors":"Shaul K. Bar-Lev,&nbsp;Gérard Letac,&nbsp;Ad Ridder","doi":"10.1007/s10463-024-00903-y","DOIUrl":"10.1007/s10463-024-00903-y","url":null,"abstract":"<div><p>The aim of this paper is to delineate a set of new classes of natural exponential families and their associated exponential dispersion models whose probability distributions are supported on the set of nonnegative integers with positive mass on 0 and 1. The new classes are obtained by considering a specific form of their variance functions. We show that the distributions of all these classes are supported on nonnegative integers, that they are infinitely divisible, and that they are skewed to the right, leptokurtic, over-dispersed, and zero-inflated (relative to the Poisson class). Accordingly, these new classes significantly enrich the set of probability models for modeling zero-inflated and over-dispersed count data. Furthermore, we elaborate on numerical techniques how to compute the distributions of our classes, and apply these to an actual data experiment.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140673175","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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