摘要
偏态分布是对称分布的一种推广,在实际生活中应用广泛,其中截断参数对界定偏态分布的边界具有重要意义.文中基于经验Bayes检验方法,研究了偏态分布截断参数的假设检验问题.考虑普通Bayes检验中先验密度的未知性和不确定性,利用递归核估计的密度函数代替未知的先验密度函数.定义检验的加权线性损失函数,从而更好地刻画了决策风险.在给定条件下证明了所提出检验函数的渐近最优性,同时给出确定的收敛速度.最后通过实例验证了文中的理论结果.
Skew distribution is a kind of generalization of the symmetric distribution and is widely applied in real life,where the truncation parameter to define the boundary of the skew distribution is of great significance.In this study,the empirical Bayes test is discussed for the truncation parameter in the skew distribution.Considering the unpredictability and uncertainty of prior density function in the common Bayes test,the unknown prior density function is estimated by the recursive kernel density function.In order to better characterize the decision risk,the weighted linear loss function of the test is defined.The asymptotic optimality of the proposed test function is proved under given conditions,and the determined convergence rates is given.Finally,the theoretical results are verified by a real example.
作者
刘蕊
谭燕
吴刘仓
LIU Rui;TAN Yan;WU Liu-cang(Faculty of Science,Kunming University of Science and Technology,Kunming 650504,China;Center of Applied Statistics,Kunming University of Science and Technology,Kunming 650504,China)
出处
《高校应用数学学报(A辑)》
北大核心
2024年第1期13-27,共15页
Applied Mathematics A Journal of Chinese Universities(Ser.A)
基金
国家自然科学基金(12261051
11861041)
昆明理工大学学术科技创新基金(2022KJ150)
昆明理工大学哲学社会科学科研创新团队(CXTD2023005)。
关键词
经验BAYES检验
偏态分布
递归核估计
渐近最优性
收敛速度
empirical Bayes test
skew distribution
recursive kernel estimation
asymptotic op-timality
convergence rates MR Subject Classification:62C12
62F05