发布求助
文献互助 智能选刊 最新文献

Metrika最新文献

筛选
英文 中文
A multivariate Jacobi polynomials regression estimator associated with an ANOVA decomposition model 与方差分解模型相关的多变量雅可比多项式回归估计器
IF 0.7 4区 数学
Metrika Pub Date : 2024-02-26 DOI: 10.1007/s00184-024-00954-4
{"title":"A multivariate Jacobi polynomials regression estimator associated with an ANOVA decomposition model","authors":"","doi":"10.1007/s00184-024-00954-4","DOIUrl":"https://doi.org/10.1007/s00184-024-00954-4","url":null,"abstract":"<h3>Abstract</h3> <p>In this work, we construct a stable and fairly fast estimator for solving multidimensional non-parametric regression problems. The proposed estimator is based on the use of a novel and special system of multivariate Jacobi polynomials that generate a basis for a reduced size of <span> <span>(d-)</span> </span>variate finite dimensional polynomials space. An ANOVA decomposition trick has been used for building this space. Also, by using some results from the theory of positive definite random matrices, we show that the proposed estimator is stable under the condition that the i.i.d. <span> <span>(d-)</span> </span>dimensional random sampling training points follow a <span> <span>(d-)</span> </span>dimensional Beta distribution. In addition, we provide the reader with an estimate for the <span> <span>(L^2-)</span> </span>risk error of the estimator. This risk error depends on the <span> <span>(L^2-)</span> </span>error of the orthogonal projection error of the regression function over the considered polynomials space. An involved study of this orthogonal projection error is done under the condition that the regression function belongs to a given weighted Sobolev space. Thanks to this novel estimate of the orthogonal projection error, we give the optimal convergence rate of our estimator. Furthermore, we give a regularized extension version of our estimator, that is capable of handling random sampling training vectors drawn according to an unknown multivariate pdf. Moreover, we derive an upper bound for the empirical risk error of this regularized estimator. Finally, we give some numerical simulations that illustrate the various theoretical results of this work. In particular, we provide simulations on a real data that compares the performance of our estimator with some existing and popular NP regression estimators.</p>","PeriodicalId":49821,"journal":{"name":"Metrika","volume":"27 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139969273","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 estimation and diagnostic of generalized linear model for insurance losses: a weighted likelihood approach 保险损失广义线性模型的稳健估计和诊断：加权似然法
IF 0.7 4区 数学
Metrika Pub Date : 2024-02-23 DOI: 10.1007/s00184-024-00952-6
Tsz Chai Fung
{"title":"Robust estimation and diagnostic of generalized linear model for insurance losses: a weighted likelihood approach","authors":"Tsz Chai Fung","doi":"10.1007/s00184-024-00952-6","DOIUrl":"https://doi.org/10.1007/s00184-024-00952-6","url":null,"abstract":"<p>This paper presents a score-based weighted likelihood estimator (SWLE) for robust estimations of the generalized linear model (GLM) for insurance loss data. The SWLE exhibits a limited sensitivity to the outliers, theoretically justifying its robustness against model contaminations. Also, with the specially designed weight function to effectively diminish the contributions of extreme losses to the GLM parameter estimations, most statistical quantities can still be derived analytically, minimizing the computational burden for parameter calibrations. Apart from robust estimations, the SWLE can also act as a quantitative diagnostic tool to detect outliers and systematic model misspecifications. Motivated by the coverage modifications which make insurance losses often random censored and truncated, the SWLE is extended to accommodate censored and truncated data. We exemplify the SWLE on three simulation studies and two real insurance datasets. Empirical results suggest that the SWLE produces more reliable parameter estimates than the MLE if outliers contaminate the dataset. The SWLE diagnostic tool also successfully detects any systematic model misspecifications with high power, accompanying some potential model improvements.</p>","PeriodicalId":49821,"journal":{"name":"Metrika","volume":"107 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139950315","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
Minimum $$theta $$ -aberration criterion for designs with qualitative and quantitative factors 具有定性和定量因素的设计的最小 $$theta $$ -aberration 标准
IF 0.7 4区 数学
Metrika Pub Date : 2024-02-23 DOI: 10.1007/s00184-024-00951-7
Liangwei Qi, Yongdao Zhou
{"title":"Minimum $$theta $$ -aberration criterion for designs with qualitative and quantitative factors","authors":"Liangwei Qi, Yongdao Zhou","doi":"10.1007/s00184-024-00951-7","DOIUrl":"https://doi.org/10.1007/s00184-024-00951-7","url":null,"abstract":"<p>The minimum aberration criterion is popular for selecting good designs with qualitative factors under an ANOVA model, and the minimum <span>(beta )</span>-aberration criterion is more suitable for selecting designs with quantitative factors under a polynomial model. However, numerous computer experiments involve both qualitative and quantitative factors, while there is a lack of a reasonable criterion to assess the effectiveness of such designs. This paper proposes some important properties of the <span>(beta )</span>-wordlength pattern for mixed-level designs, and introduces the minimum <span>(theta )</span>-aberration criterion for comparing and selecting designs with qualitative and quantitative factors based on a full model involving all interactions of the factors. The computation of the <span>(theta )</span>-wordlength pattern is optimized by the generalized wordlength enumerator. Then we provide some construction methods for designs with less <span>(theta )</span>-aberration, and apply this criterion to screen the marginally coupled designs and the doubly coupled designs.</p>","PeriodicalId":49821,"journal":{"name":"Metrika","volume":"14 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139950588","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
Bayesian composite $$L^p$$ -quantile regression 贝叶斯综合 $$L^p$$ -quantile 回归
IF 0.7 4区 数学
Metrika Pub Date : 2024-02-21 DOI: 10.1007/s00184-024-00950-8
{"title":"Bayesian composite $$L^p$$ -quantile regression","authors":"","doi":"10.1007/s00184-024-00950-8","DOIUrl":"https://doi.org/10.1007/s00184-024-00950-8","url":null,"abstract":"<h3>Abstract</h3> <p><span> <span>(L^p)</span> </span>-quantiles are a class of generalized quantiles defined as minimizers of an asymmetric power function. They include both quantiles, <span> <span>(p=1)</span> </span>, and expectiles, <span> <span>(p=2)</span> </span>, as special cases. This paper studies composite <span> <span>(L^p)</span> </span>-quantile regression, simultaneously extending single <span> <span>(L^p)</span> </span>-quantile regression and composite quantile regression. A Bayesian approach is considered, where a novel parameterization of the skewed exponential power distribution is utilized. Further, a Laplace prior on the regression coefficients allows for variable selection. Through a Monte Carlo study and applications to empirical data, the proposed method is shown to outperform Bayesian composite quantile regression in most aspects.</p>","PeriodicalId":49821,"journal":{"name":"Metrika","volume":"77 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139921337","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 beta regression through the logit transformation 通过对数转换实现稳健的贝塔回归
IF 0.7 4区 数学
Metrika Pub Date : 2024-02-18 DOI: 10.1007/s00184-024-00949-1
Yuri S. Maluf, Silvia L. P. Ferrari, Francisco F. Queiroz
{"title":"Robust beta regression through the logit transformation","authors":"Yuri S. Maluf, Silvia L. P. Ferrari, Francisco F. Queiroz","doi":"10.1007/s00184-024-00949-1","DOIUrl":"https://doi.org/10.1007/s00184-024-00949-1","url":null,"abstract":"<p>Beta regression models are employed to model continuous response variables in the unit interval, like rates, percentages, or proportions. Their applications rise in several areas, such as medicine, environment research, finance, and natural sciences. The maximum likelihood estimation is widely used to make inferences for the parameters. Nonetheless, it is well-known that the maximum likelihood-based inference suffers from the lack of robustness in the presence of outliers. Such a case can bring severe bias and misleading conclusions. Recently, robust estimators for beta regression models were presented in the literature. However, these estimators require non-trivial restrictions in the parameter space, which limit their application. This paper develops new robust estimators that overcome this drawback. Their asymptotic and robustness properties are studied, and robust Wald-type tests are introduced. Simulation results evidence the merits of the new robust estimators. Inference and diagnostics using the new estimators are illustrated in an application to health insurance coverage data. The new R package robustbetareg is introduced.</p>","PeriodicalId":49821,"journal":{"name":"Metrika","volume":"7 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139921323","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 Bayesian predictive density estimation for skew-normal distributions 关于倾斜正态分布的贝叶斯预测密度估计
IF 0.7 4区 数学
Metrika Pub Date : 2024-02-17 DOI: 10.1007/s00184-024-00946-4
Othmane Kortbi
{"title":"On Bayesian predictive density estimation for skew-normal distributions","authors":"Othmane Kortbi","doi":"10.1007/s00184-024-00946-4","DOIUrl":"https://doi.org/10.1007/s00184-024-00946-4","url":null,"abstract":"<p>This paper is concerned with prediction for skew-normal models, and more specifically the Bayes estimation of a predictive density for <span>(Y left. right| mu sim {mathcal {S}} {mathcal {N}}_p (mu , v_y I_p, lambda ))</span> under Kullback–Leibler loss, based on <span>(X left. right| mu sim {mathcal {S}} {mathcal {N}}_p (mu , v_x I_p, lambda ))</span> with known dependence and skewness parameters. We obtain representations for Bayes predictive densities, including the minimum risk equivariant predictive density <span>(hat{p}_{pi _{o}})</span> which is a Bayes predictive density with respect to the noninformative prior <span>(pi _0equiv 1)</span>. George et al. (Ann Stat 34:78–91, 2006) used the parallel between the problem of point estimation and the problem of estimation of predictive densities to establish a connection between the difference of risks of the two problems. The development of similar connection, allows us to determine sufficient conditions of dominance over <span>(hat{p}_{pi _{o}})</span> and of minimaxity. First, we show that <span>(hat{p}_{pi _{o}})</span> is a minimax predictive density under KL risk for the skew-normal model. After this, for dimensions <span>(pge 3)</span>, we obtain classes of Bayesian minimax densities that improve <span>(hat{p}_{pi _{o}})</span> under KL loss, for the subclass of skew-normal distributions with small value of skewness parameter. Moreover, for dimensions <span>(pge 4)</span>, we obtain classes of Bayesian minimax densities that improve <span>(hat{p}_{pi _{o}})</span> under KL loss, for the whole class of skew-normal distributions. Examples of proper priors, including generalized student priors, generating Bayesian minimax densities that improve <span>(hat{p}_{pi _{o}})</span> under KL loss, were constructed when <span>(pge 5)</span>. This findings represent an extension of Liang and Barron (IEEE Trans Inf Theory 50(11):2708–2726, 2004), George et al. (Ann Stat 34:78–91, 2006) and Komaki (Biometrika 88(3):859–864, 2001) results to a subclass of asymmetrical distributions.\u0000</p>","PeriodicalId":49821,"journal":{"name":"Metrika","volume":"6 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139772832","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
Pointwise density estimation on metric spaces and applications in seismology 度量空间上的点式密度估计及其在地震学中的应用
IF 0.7 4区 数学
Metrika Pub Date : 2024-02-13 DOI: 10.1007/s00184-024-00948-2
G. Cleanthous, Athanasios G. Georgiadis, P. A. White
{"title":"Pointwise density estimation on metric spaces and applications in seismology","authors":"G. Cleanthous, Athanasios G. Georgiadis, P. A. White","doi":"10.1007/s00184-024-00948-2","DOIUrl":"https://doi.org/10.1007/s00184-024-00948-2","url":null,"abstract":"<p>We are studying the problem of estimating density in a wide range of metric spaces, including the Euclidean space, the sphere, the ball, and various Riemannian manifolds. Our framework involves a metric space with a doubling measure and a self-adjoint operator, whose heat kernel exhibits Gaussian behaviour. We begin by reviewing the construction of kernel density estimators and the related background information. As a novel result, we present a pointwise kernel density estimation for probability density functions that belong to general Hölder spaces. The study is accompanied by an application in Seismology. Precisely, we analyze a globally-indexed dataset of earthquake occurrence and compare the out-of-sample performance of several approximated kernel density estimators indexed on the sphere.</p>","PeriodicalId":49821,"journal":{"name":"Metrika","volume":"91 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139758206","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
Stochastic comparisons, differential entropy and varentropy for distributions induced by probability density functions 概率密度函数诱导分布的随机比较、差分熵和熵
IF 0.7 4区 数学
Metrika Pub Date : 2024-02-09 DOI: 10.1007/s00184-024-00947-3
{"title":"Stochastic comparisons, differential entropy and varentropy for distributions induced by probability density functions","authors":"","doi":"10.1007/s00184-024-00947-3","DOIUrl":"https://doi.org/10.1007/s00184-024-00947-3","url":null,"abstract":"<h3>Abstract</h3> <p>Stimulated by the need of describing useful notions related to information measures, we introduce the ‘pdf-related distributions’. These are defined in terms of transformation of absolutely continuous random variables through their own probability density functions. We investigate their main characteristics, with reference to the general form of the distribution, the quantiles, and some related notions of reliability theory. This allows us to obtain a characterization of the pdf-related distribution being uniform for distributions of exponential and Laplace type as well. We also face the problem of stochastic comparing the pdf-related distributions by resorting to suitable stochastic orders. Finally, the given results are used to analyse properties and to compare some useful information measures, such as the differential entropy and the varentropy.</p>","PeriodicalId":49821,"journal":{"name":"Metrika","volume":"18 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139758426","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 Berry–Esséen bound of frequency polygon estimation under $$rho $$ -mixing samples 论 $$rho $$ 混合样本下频率多边形估计的 Berry-Esséen 边界
IF 0.7 4区 数学
Metrika Pub Date : 2024-02-06 DOI: 10.1007/s00184-023-00944-y
Yi Wu, Xuejun Wang
{"title":"On Berry–Esséen bound of frequency polygon estimation under $$rho $$ -mixing samples","authors":"Yi Wu, Xuejun Wang","doi":"10.1007/s00184-023-00944-y","DOIUrl":"https://doi.org/10.1007/s00184-023-00944-y","url":null,"abstract":"<p>The frequency polygon estimation, which is based on histogram technique, has similar convergence rate as those of non-negative kernel estimators and the advantages of computational simplicity. This work will study the Berry–Esséen bound of frequency polygon estimation with <span>(rho )</span>-mixing samples under some general conditions. The rates are shown to be <span>(O(n^{-1/9}))</span> if the mixing coefficients decay polynomially and <span>(O(n^{-1/6}log ^{1/3}n))</span> if the mixing coefficients decay geometrically. These results improve and extend the corresponding ones in the literature and reveal that the frequency polygon estimator also has similar Berry–Esséen bound as those of kernel estimators. Moreover, some numerical analysis is also presented to assess the finite sample performance of the theoretical results.</p>","PeriodicalId":49821,"journal":{"name":"Metrika","volume":"124 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139758084","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
Measure of deviancy from marginal mean equality based on cumulative marginal probabilities in square contingency tables 基于方形或然率表中累积边际概率的边际均值偏离度量
IF 0.7 4区 数学
Metrika Pub Date : 2024-02-05 DOI: 10.1007/s00184-023-00945-x
Shuji Ando
{"title":"Measure of deviancy from marginal mean equality based on cumulative marginal probabilities in square contingency tables","authors":"Shuji Ando","doi":"10.1007/s00184-023-00945-x","DOIUrl":"https://doi.org/10.1007/s00184-023-00945-x","url":null,"abstract":"<p>This study proposes a measure that can concurrently evaluate the degree and direction of deviancy from the marginal mean equality (ME) model in square contingency tables with ordered categories. The proposed measure is constructed as the function of the row and column cumulative marginal probabilities. When the ME model does not fit data, we are interested in measuring the degree of deviancy from the ME model, because the model having weaker restrictions than the ME model is only the saturated model. This existing measure, which represents the degree of deviancy from the ME model, does not depend on the probabilities that observations will fall in the main diagonal cells of the table. For the data in which observations are concentrated in the main diagonal cells, the existing measure may overestimate the degree of deviancy from the ME model. The proposed measure can address this issue. This study derives an estimator and an approximate confidence interval for the proposed measure using the delta method. The proposed measure would be utility for comparing degrees of deviancy from the ME model in two datasets. The proposed measure is evaluated the usefulness with the application to real data of clinical trials.</p>","PeriodicalId":49821,"journal":{"name":"Metrika","volume":"6 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139758331","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
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信