首页    期刊浏览 2024年11月26日 星期二
登录注册

文章基本信息

  • 标题:Median confidence regions in a nonparametric model
  • 本地全文:下载
  • 作者:Edsel A. Peña ; Taeho Kim
  • 期刊名称:Electronic Journal of Statistics
  • 印刷版ISSN:1935-7524
  • 出版年度:2019
  • 卷号:13
  • 期号:2
  • 页码:2348-2390
  • DOI:10.1214/19-EJS1577
  • 语种:English
  • 出版社:Institute of Mathematical Statistics
  • 摘要:The nonparametric measurement error model (NMEM) postulates that $X_{i}=\Delta +\epsilon _{i},i=1,2,\ldots ,n;\Delta \in \Re $ with $\epsilon _{i},i=1,2,\ldots ,n$, IID from $F(\cdot )\in\mathfrak{F}_{c,0}$, where $\mathfrak{F}_{c,0}$ is the class of all continuous distributions with median $0$, so $\Delta $ is the median parameter of $X$. This paper deals with the problem of constructing a confidence region (CR) for $\Delta $ under the NMEM. Aside from the NMEM, the problem setting also arises in a variety of situations, including inference about the median lifetime of a complex system arising in engineering, reliability, biomedical, and public health settings, as well as in the economic arena such as when dealing with household income. Current methods of constructing CRs for $\Delta $ are discussed, including the $T$-statistic based CR and the Wilcoxon signed-rank statistic based CR, arguably the two default methods in applied work when a confidence interval about the center of a distribution is desired. A ‘bottom-to-top’ approach for constructing CRs is implemented, which starts by imposing reasonable invariance or equivariance conditions on the desired CRs, and then optimizing with respect to their mean contents on subclasses of $\mathfrak{F}_{c,0}$. This contrasts with the usual approach of using a pivotal quantity constructed from test statistics and/or estimators and then ‘pivoting’ to obtain the CR. Applications to a real car mileage data set and to Proschan’s famous air-conditioning data set are illustrated. Simulation studies to compare performances of the different CR methods were performed. Results of these studies indicate that the sign-statistic based CR and the optimal CR focused on symmetric distributions satisfy the confidence level requirement, though they tended to have higher contents; while three of the bootstrap-based CR procedures and one of the newly-developed adaptive CR tended to be a tad more liberal, but with smaller contents. A critical recommendation for practitioners is that, under the NMEM, the $T$-statistic based and Wilcoxon signed-rank statistic based CRs should not be used since they either have very degraded coverage probabilities or inflated contents under some of the allowable error distributions under the NMEM.
国家哲学社会科学文献中心版权所有