部分线性尾指数模型的b样条有效估计

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Australian & New Zealand Journal of Statistics Pub Date : 2022-02-02 DOI:10.1111/anzs.12357

Yaolan Ma, Bo Wei

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引用次数: 0

摘要

尾指数是极值理论中的一个重要参数。本文考虑了部分线性尾指数模型的一种简单而灵活的样条估计方法。我们用b样条近似未知函数，构造一个近似对数似然函数来估计线性协变量和b样条基函数的系数。建立了估计量的相合性和渐近正态性。随后，通过对Fremantle年最高海平面数据和芝加哥空气污染数据的模拟和应用说明了所提出的方法。

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Efficient estimation of partially linear tail index models using B-splines

The tail index is an important parameter in extreme value theory. In this paper, we consider a simple yet flexible spline estimation method for partially linear tail index models. We approximate the unknown function by B-splines and construct an approximate log-likelihood function to estimate the coefficients of the linear covariates and the B-spline basis functions. Consistency and asymptotic normality of the estimators are established. Subsequently, the proposed method is illustrated by using simulations and applications to the Fremantle annual maximum sea levels data and Chicago air pollution data.

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来源期刊

Australian & New Zealand Journal of Statistics 数学-统计学与概率论

CiteScore

1.30

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Australian & New Zealand Journal of Statistics is an international journal managed jointly by the Statistical Society of Australia and the New Zealand Statistical Association. Its purpose is to report significant and novel contributions in statistics, ranging across articles on statistical theory, methodology, applications and computing. The journal has a particular focus on statistical techniques that can be readily applied to real-world problems, and on application papers with an Australasian emphasis. Outstanding articles submitted to the journal may be selected as Discussion Papers, to be read at a meeting of either the Statistical Society of Australia or the New Zealand Statistical Association. The main body of the journal is divided into three sections. The Theory and Methods Section publishes papers containing original contributions to the theory and methodology of statistics, econometrics and probability, and seeks papers motivated by a real problem and which demonstrate the proposed theory or methodology in that situation. There is a strong preference for papers motivated by, and illustrated with, real data. The Applications Section publishes papers demonstrating applications of statistical techniques to problems faced by users of statistics in the sciences, government and industry. A particular focus is the application of newly developed statistical methodology to real data and the demonstration of better use of established statistical methodology in an area of application. It seeks to aid teachers of statistics by placing statistical methods in context. The Statistical Computing Section publishes papers containing new algorithms, code snippets, or software descriptions (for open source software only) which enhance the field through the application of computing. Preference is given to papers featuring publically available code and/or data, and to those motivated by statistical methods for practical problems.