IF 0.7 4区数学

Metrika Pub Date : 2024-03-05 DOI: 10.1007/s00184-024-00956-2

Andrea C. Garcia-Angulo, Gerda Claeskens

引用次数: 0

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> 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 (d-) 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. (d-) dimensional random sampling training points follow a (d-) dimensional Beta distribution. In addition, we provide the reader with an estimate for the (L^2-) risk error of the estimator. This risk error depends on the (L^2-) 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.","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":"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.","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

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

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

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":"This paper is concerned with prediction for skew-normal models, and more specifically the Bayes estimation of a predictive density for (Y left. right| mu sim {mathcal {S}} {mathcal {N}}_p (mu , v_y I_p, lambda )) under Kullback–Leibler loss, based on (X left. right| mu sim {mathcal {S}} {mathcal {N}}_p (mu , v_x I_p, lambda )) with known dependence and skewness parameters. We obtain representations for Bayes predictive densities, including the minimum risk equivariant predictive density (hat{p}_{pi _{o}}) which is a Bayes predictive density with respect to the noninformative prior (pi _0equiv 1). 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 (hat{p}_{pi _{o}}) and of minimaxity. First, we show that (hat{p}_{pi _{o}}) is a minimax predictive density under KL risk for the skew-normal model. After this, for dimensions (pge 3), we obtain classes of Bayesian minimax densities that improve (hat{p}_{pi _{o}}) under KL loss, for the subclass of skew-normal distributions with small value of skewness parameter. Moreover, for dimensions (pge 4), we obtain classes of Bayesian minimax densities that improve (hat{p}_{pi _{o}}) 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 (hat{p}_{pi _{o}}) under KL loss, were constructed when (pge 5). 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","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

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

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":"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.","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

Nonparametric estimation of $${mathbb {P}}(X 对 $${mathbb {P}}(X) 的非参数估计

IF 0.7 4区数学

Metrika Pub Date : 2024-01-08 DOI: 10.1007/s00184-023-00941-1

Cao Xuan Phuong, Le Thi Hong Thuy

{"title":"Nonparametric estimation of $${mathbb {P}}(X","authors":"Cao Xuan Phuong, Le Thi Hong Thuy","doi":"10.1007/s00184-023-00941-1","DOIUrl":"https://doi.org/10.1007/s00184-023-00941-1","url":null,"abstract":"Let X, Y be continuous random variables with unknown distributions. The aim of this paper is to study the problem of estimating the probability (theta := {mathbb {P}}(X<Y)) based on independent random samples from the distributions of (X'), (Y'), (zeta ) and (eta ), where (X' = X + zeta ), (Y' = Y + eta ) and X, Y, (zeta ), (eta ) are mutually independent random variables. In this context, (zeta ), (eta ) are referred to as measurement errors. We apply the ridge-parameter regularization method to derive a nonparametric estimator for (theta ) depending on two parameters. Our estimator is shown to be consistent with respect to mean squared error if the characteristic functions of (zeta ), (eta ) only vanish on Lebesgue measure zero sets. Under some further assumptions on the densities of X, Y, (zeta ) and (eta ), we obtain some upper and lower bounds on the convergence rate of the estimator. A numerical example is also given to illustrate the efficiency of our method.","PeriodicalId":49821,"journal":{"name":"Metrika","volume":"216 3 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139408140","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

The local linear functional kNN estimator of the conditional expectile: uniform consistency in number of neighbors 条件期望值的局部线性函数 kNN 估计器：邻域数的均匀一致性

IF 0.7 4区数学

Metrika Pub Date : 2024-01-06 DOI: 10.1007/s00184-023-00942-0

Ibrahim M. Almanjahie, Salim Bouzebda, Zoulikha Kaid, Ali Laksaci

引用次数: 0

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