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Smoothed partially linear varying coefficient quantile regression with nonignorable missing response 具有不可忽略的缺失响应的平滑部分线性变化系数量化回归
IF 0.7 4区 数学
Metrika Pub Date : 2024-09-19 DOI: 10.1007/s00184-024-00974-0
Xiaowen Liang, Boping Tian, Lijian Yang
{"title":"Smoothed partially linear varying coefficient quantile regression with nonignorable missing response","authors":"Xiaowen Liang, Boping Tian, Lijian Yang","doi":"10.1007/s00184-024-00974-0","DOIUrl":"https://doi.org/10.1007/s00184-024-00974-0","url":null,"abstract":"<p>In this paper, we propose a smoothed quantile regression estimator and variable selection procedure for partially linear varying coefficient models with nonignorable nonresponse. To avoid the computational problem caused by the non-smooth quantile loss function, we employ the kernel smoothing method. To address the identifiability issue, we use an instrument and estimate the parametric propensity function based on the generalized method of moments. Once the propensity is estimated, we construct the bias-corrected estimating equations utilizing the inverse probability weighting approach. Then, we apply the empirical likelihood method to obtain an unbiased estimator. The asymptotic properties of the proposed estimators are established for both the parametric and nonparametric parts. Meanwhile, variable selection is considered by using the SCAD penalty. The finite-sample performance of the estimators is studied through simulations, and a real-data example is also presented.</p>","PeriodicalId":49821,"journal":{"name":"Metrika","volume":"119 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142268964","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
Two-stage and purely sequential minimum risk point estimation of the scale parameter of a family of distributions under modified LINEX loss plus sampling cost 在修正的 LINEX 损失加抽样成本条件下，对分布系列的规模参数进行两阶段和纯顺序最小风险点估计
IF 0.7 4区 数学
Metrika Pub Date : 2024-09-12 DOI: 10.1007/s00184-024-00973-1
Neeraj Joshi, Sudeep R. Bapat, Raghu Nandan Sengupta
{"title":"Two-stage and purely sequential minimum risk point estimation of the scale parameter of a family of distributions under modified LINEX loss plus sampling cost","authors":"Neeraj Joshi, Sudeep R. Bapat, Raghu Nandan Sengupta","doi":"10.1007/s00184-024-00973-1","DOIUrl":"https://doi.org/10.1007/s00184-024-00973-1","url":null,"abstract":"<p>In this research, we present two-stage and purely sequential methodologies for estimating the scale parameter of the Moore and Bilikam family of lifetime distributions (see Moore and Bilikam in IEEE Trans Reliabil 27:64–67, 1978). We propose our methodologies under the minimum risk point estimation setup, whereby we consider the modified LINEX loss function plus non linear sampling cost. We study some interesting exact distributional properties associated with our stopping rules. We also present simulation analyses using Weibull distribution (special case of the Moore and Bilikam family) to check the performance of our two-stage and purely sequential procedures. Finally, we provide a real data set from COVID-19 and analyze it using the Weibull model in support of the practical utility of our proposed two-stage methodology.</p>","PeriodicalId":49821,"journal":{"name":"Metrika","volume":"18 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142208154","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
Mean test for high-dimensional data based on covariance matrix with linear structures 基于线性结构协方差矩阵的高维数据均值检验
IF 0.7 4区 数学
Metrika Pub Date : 2024-07-02 DOI: 10.1007/s00184-024-00971-3
Guanpeng Wang, Yuyuan Wang, Hengjian Cui
{"title":"Mean test for high-dimensional data based on covariance matrix with linear structures","authors":"Guanpeng Wang, Yuyuan Wang, Hengjian Cui","doi":"10.1007/s00184-024-00971-3","DOIUrl":"https://doi.org/10.1007/s00184-024-00971-3","url":null,"abstract":"<p>In this work, the mean test is considered under the condition that the number of dimensions <i>p</i> is much larger than the sample size <i>n</i> when the covariance matrix is represented as a linear structure as possible. At first, the estimator of coefficients in the linear structures of the covariance matrix is constructed, and then an efficient covariance matrix estimator is naturally given. Next, a new test statistic similar to the classical Hotelling’s <span>(T^2)</span> test is proposed by replacing the sample covariance matrix with the given estimator of covariance matrix. Then the asymptotic normality of the estimator of coefficients and that of a new statistic for the mean test are separately obtained under some mild conditions. Simulation results show that the performance of the proposed test statistic is almost the same as the Hotelling’s <span>(T^2)</span> test statistic for which the covariance matrix is known. Our new test statistic can not only control reasonably the nominal level; it also gains greater empirical powers than competing tests. It is found that the power of mean test has great improvement when considering the structure information of the covariance matrix, especially for high-dimensional cases. Moreover, an example with real data is provided to show the application of our approach.</p>","PeriodicalId":49821,"journal":{"name":"Metrika","volume":"156 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141511744","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
Statistical inference for linear quantile regression with measurement error in covariates and nonignorable missing responses 具有协变量测量误差和不可忽略的缺失响应的线性量回归的统计推断
IF 0.7 4区 数学
Metrika Pub Date : 2024-05-18 DOI: 10.1007/s00184-024-00967-z
Xiaowen Liang, Boping Tian
{"title":"Statistical inference for linear quantile regression with measurement error in covariates and nonignorable missing responses","authors":"Xiaowen Liang, Boping Tian","doi":"10.1007/s00184-024-00967-z","DOIUrl":"https://doi.org/10.1007/s00184-024-00967-z","url":null,"abstract":"<p>In this paper, we consider quantile regression estimation for linear models with covariate measurement errors and nonignorable missing responses. Firstly, the influence of measurement errors is eliminated through the bias-corrected quantile loss function. To handle the identifiability issue in the nonignorable missing, a nonresponse instrument is used. Then, based on the inverse probability weighting approach, we propose a weighted bias-corrected quantile loss function that can handle both nonignorable missingness and covariate measurement errors. Under certain regularity conditions, we establish the asymptotic properties of the proposed estimators. The finite sample performance of the proposed method is illustrated by Monte Carlo simulations and an empirical data analysis.</p>","PeriodicalId":49821,"journal":{"name":"Metrika","volume":"47 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141060085","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
Sparse-penalized deep neural networks estimator under weak dependence 弱依赖性下的稀疏惩罚性深度神经网络估计器
IF 0.7 4区 数学
Metrika Pub Date : 2024-04-23 DOI: 10.1007/s00184-024-00965-1
William Kengne, Modou Wade
{"title":"Sparse-penalized deep neural networks estimator under weak dependence","authors":"William Kengne, Modou Wade","doi":"10.1007/s00184-024-00965-1","DOIUrl":"https://doi.org/10.1007/s00184-024-00965-1","url":null,"abstract":"<p>We consider the nonparametric regression and the classification problems for <span>(psi )</span>-weakly dependent processes. This weak dependence structure is more general than conditions such as, mixing, association<span>(cdots )</span> A penalized estimation method for sparse deep neural networks is performed. In both nonparametric regression and binary classification problems, we establish oracle inequalities for the excess risk of the sparse-penalized deep neural networks estimators. Convergence rates of the excess risk of these estimators are also derived. The simulation results displayed show that, the proposed estimators can work well than the non penalized estimators, and that, there is a gain of using this estimator.</p>","PeriodicalId":49821,"journal":{"name":"Metrika","volume":"34 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140806465","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
Structure of hybrid censoring schemes and its implications 混合剔除方案的结构及其影响
IF 0.7 4区 数学
Metrika Pub Date : 2024-04-09 DOI: 10.1007/s00184-024-00960-6
Erhard Cramer
{"title":"Structure of hybrid censoring schemes and its implications","authors":"Erhard Cramer","doi":"10.1007/s00184-024-00960-6","DOIUrl":"https://doi.org/10.1007/s00184-024-00960-6","url":null,"abstract":"<p>In this paper, structural properties of (progressive) hybrid censoring schemes are established by studying the possible data scenarios resulting from the hybrid censoring scheme. The results illustrate that the distributions of hybrid censored random variables can be immediately derived from the cases of Type-I and Type-II censored data. Furthermore, it turns out that results in likelihood and Bayesian inference are also obtained directly which explains the similarities present in the probabilistic and statistical analysis of these censoring schemes. The power of the approach is illustrated by applying the approach to the quite complex unified Type-II (progressive) hybrid censoring scheme. Finally, it is shown that the approach is not restricted to (progressively Type-II censored) order statistics and that it can be extended to almost any kind of ordered data.</p>","PeriodicalId":49821,"journal":{"name":"Metrika","volume":"18 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140565959","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
Variance estimation for average treatment effects estimated by g-computation 通过 g 计算估计的平均治疗效果的方差估计
IF 0.7 4区 数学
Metrika Pub Date : 2024-04-06 DOI: 10.1007/s00184-024-00962-4
Stefan Nygaard Hansen, Morten Overgaard
{"title":"Variance estimation for average treatment effects estimated by g-computation","authors":"Stefan Nygaard Hansen, Morten Overgaard","doi":"10.1007/s00184-024-00962-4","DOIUrl":"https://doi.org/10.1007/s00184-024-00962-4","url":null,"abstract":"<p>The average treatment effect is used to evaluate effects of interventions in a population. Under certain causal assumptions, such an effect may be estimated from observational data using the g-computation technique. The asymptotic properties of this estimator appears not to be well-known and hence bootstrapping has become the preferred method for estimating its variance. Bootstrapping is, however, not an optimal choice for multiple reasons; it is a slow procedure and, if based on too few bootstrap samples, results in a highly variable estimator of the variance. In this paper, we consider estimators of potential outcome means and average treatment effects using g-computation. We consider these parameters for the entire population but also in subgroups, for example, the average treatment effect among the treated. We derive their asymptotic distributions in a general framework. An estimator of the asymptotic variance is proposed and shown to be consistent when g-computation is used in conjunction with the M-estimation technique. The proposed estimator is shown to be superior to the bootstrap technique in a simulation study. Robustness against model misspecification is also demonstrated by means of simulations.</p>","PeriodicalId":49821,"journal":{"name":"Metrika","volume":"17 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140565849","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
Bahadur representations for the bootstrap median absolute deviation and the application to projection depth weighted mean 自举绝对偏差中值的巴哈杜尔表示法及其在投影深度加权平均值中的应用
IF 0.7 4区 数学
Metrika Pub Date : 2024-03-19 DOI: 10.1007/s00184-024-00958-0
Qing Liu, Xiaohui Liu, Zihao Hu
{"title":"Bahadur representations for the bootstrap median absolute deviation and the application to projection depth weighted mean","authors":"Qing Liu, Xiaohui Liu, Zihao Hu","doi":"10.1007/s00184-024-00958-0","DOIUrl":"https://doi.org/10.1007/s00184-024-00958-0","url":null,"abstract":"<p>Median absolute deviation (hereafter MAD) is known as a robust alternative to the ordinary variance. It has been widely utilized to induce robust statistical inferential procedures. In this paper, we investigate the strong and weak Bahadur representations of its bootstrap counterpart. As a useful application, we utilize the results to derive the weak Bahadur representation of the bootstrap sample projection depth weighted mean—a quite important location estimator depending on MAD.\u0000</p>","PeriodicalId":49821,"journal":{"name":"Metrika","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140168772","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
Measures of kurtosis: inadmissible for asymmetric distributions? 峰度测量：非对称分布不允许？
IF 0.7 4区 数学
Metrika Pub Date : 2024-03-17 DOI: 10.1007/s00184-024-00959-z
Andreas Eberl, Bernhard Klar
{"title":"Measures of kurtosis: inadmissible for asymmetric distributions?","authors":"Andreas Eberl, Bernhard Klar","doi":"10.1007/s00184-024-00959-z","DOIUrl":"https://doi.org/10.1007/s00184-024-00959-z","url":null,"abstract":"<p>Skewness and kurtosis are natural characteristics of a distribution. While it has long been recognized that they are more intrinsically entangled than other characteristics like location and dispersion, this has recently been made more explicit by Eberl and Klar (Stat Papers 65:415–433, 2024) with regard to orders of kurtosis. In this paper, we analyze the implications of this entanglement on kurtosis measures in general and for several specific examples. As a key finding, we show that kurtosis measures that are defined in the classical order-based way, which is analogous to measures of location, dispersion and skewness, do not exist. This raises serious doubts about the frequent application of such measures to skewed data. We then consider old and new proposals for kurtosis measures and evaluate under which additional conditions they measure kurtosis in a meaningful way. Some measures also allow more specific representations of the influence of skewness on the measurement of kurtosis than are available in a general setting. This works particularly well for a family of newly introduced density-based kurtosis measures.\u0000</p>","PeriodicalId":49821,"journal":{"name":"Metrika","volume":"2013 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140156658","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
Right-censored nonparametric regression with measurement error 有测量误差的右删失非参数回归
IF 0.7 4区 数学
Metrika Pub Date : 2024-03-05 DOI: 10.1007/s00184-024-00953-5
Dursun Aydın, Ersin Yılmaz, Nur Chamidah, Budi Lestari, I. Nyoman Budiantara
{"title":"Right-censored nonparametric regression with measurement error","authors":"Dursun Aydın, Ersin Yılmaz, Nur Chamidah, Budi Lestari, I. Nyoman Budiantara","doi":"10.1007/s00184-024-00953-5","DOIUrl":"https://doi.org/10.1007/s00184-024-00953-5","url":null,"abstract":"<p>This study focuses on estimating a nonparametric regression model with right-censored data when the covariate is subject to measurement error. To achieve this goal, it is necessary to solve the problems of censorship and measurement error ignored by many researchers. Note that the presence of measurement errors causes biased and inconsistent parameter estimates. Moreover, non-parametric regression techniques cannot be applied directly to right-censored observations. In this context, we consider an updated response variable using the Buckley–James method (BJM), which is essentially based on the Kaplan–Meier estimator, to solve the censorship problem. Then the measurement error problem is handled using the kernel deconvolution method, which is a specialized tool to solve this problem. Accordingly, three denconvoluted estimators based on BJM are introduced using kernel smoothing, local polynomial smoothing, and B-spline techniques that incorporate both the updated response variable and kernel deconvolution.The performances of these estimators are compared in a detailed simulation study. In addition, a real-world data example is presented using the Covid-19 dataset.</p>","PeriodicalId":49821,"journal":{"name":"Metrika","volume":"32 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140043951","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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