二元模型中阶限位置和尺度参数的成分等变估计:一个统一的研究

IF 0.6 4区 数学 Q4 STATISTICS & PROBABILITY Brazilian Journal of Probability and Statistics Pub Date : 2021-09-30 DOI:10.1214/23-bjps562
Naresh Garg, N. Misra
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引用次数: 3

摘要

当两个分布之间的顺序已知(例如$\theta_1\leq \theta_2$)时,估计它们的位置(尺度)参数$\theta_1$和$\theta_2$的问题已经在文献中得到了广泛的研究。这些研究中的许多都集中在通过利用$\theta_1 \leq \theta_2$的先验信息,在无限制的情况下,推导支配最佳位置(尺度)等变估计量的估计量。其中一些研究考虑了特定的分布,使得相关的随机变量在统计上是独立的。本文考虑一种一般的二元模型和一般损失函数,并将文献证明的各种结果统一起来。我们还考虑了这些结果在二元正态和Cheriyan和Ramabhadran二元模型中的应用。本文还考虑了一个模拟研究,比较了各种估计器在二元正态和Cheriyan和Ramabhadran的二元伽玛模型下的风险表现。
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Componentwise equivariant estimation of order restricted location and scale parameters in bivariate models: A unified study
The problem of estimating location (scale) parameters $\theta_1$ and $\theta_2$ of two distributions when the ordering between them is known apriori (say, $\theta_1\leq \theta_2$) has been extensively studied in the literature. Many of these studies are centered around deriving estimators that dominate the best location (scale) equivariant estimators, for the unrestricted case, by exploiting the prior information that $\theta_1 \leq \theta_2$. Several of these studies consider specific distributions such that the associated random variables are statistically independent. This paper considers a general bivariate model and general loss function and unifies various results proved in the literature. We also consider applications of these results to a bivariate normal and a Cheriyan and Ramabhadran's bivariate gamma model. A simulation study is also considered to compare the risk performances of various estimators under bivariate normal and Cheriyan and Ramabhadran's bivariate gamma models.
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来源期刊
CiteScore
1.60
自引率
10.00%
发文量
30
审稿时长
>12 weeks
期刊介绍: The Brazilian Journal of Probability and Statistics aims to publish high quality research papers in applied probability, applied statistics, computational statistics, mathematical statistics, probability theory and stochastic processes. More specifically, the following types of contributions will be considered: (i) Original articles dealing with methodological developments, comparison of competing techniques or their computational aspects. (ii) Original articles developing theoretical results. (iii) Articles that contain novel applications of existing methodologies to practical problems. For these papers the focus is in the importance and originality of the applied problem, as well as, applications of the best available methodologies to solve it. (iv) Survey articles containing a thorough coverage of topics of broad interest to probability and statistics. The journal will occasionally publish book reviews, invited papers and essays on the teaching of statistics.
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