| 随机受控分支过程中繁衍变量均值的经验似然估计 |
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| 引用本文： | 张水胜,宇世航.随机受控分支过程中繁衍变量均值的经验似然估计[J].数学的实践与认识,2020(6):299-304. |
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| 作者姓名： | 张水胜 宇世航 |
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| 作者单位： | 齐齐哈尔大学理学院 |
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| 基金项目： | 齐齐哈尔市软科学项目(RKX-201712)黑龙江省教育厅基本业务专项(135209247,135309477);黑龙江省高等教育教学改革项目(SJGY20170381)。 |
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| 摘 要： | 文章研究受控分支过程在随机环境下的繁衍变量均值的估计问题.我们基于加权条件最小二乘法构造估计方程,发展了一个经验似然比检验,并证明了这个检验统计量的极限分布是χ^2分布.最后通过随机模拟验证了经验似然方法有较高的覆盖概率.
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| 关 键 词： | 分支过程 随机受控函数 经验似然 加权条件最小二乘 |
Empirical Likelihood of the Offspring Mean in a Controlled Branching Process with a Random Control Function |
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| ZHANG Shui-sheng,YU Shi-hang.Empirical Likelihood of the Offspring Mean in a Controlled Branching Process with a Random Control Function[J].Mathematics in Practice and Theory,2020(6):299-304. |
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| Authors: | ZHANG Shui-sheng YU Shi-hang |
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| Institution: | (Department of Maths,Qiqihar University,Qiqihar 161006,China) |
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| Abstract: | In this article,we consider the parameter estimationof the offspring mean in a controlled branching process with a random control function.We construct an estimation equation based on the weighted condition least square estimation,develop an empirical likelihood ratio test,and prove its asymptotic distribution is a standardχ^2.Furthermore,Simulation results indicate that the proposed method works well for practical situations. |
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| Keywords: | branching processes random control function empirical likelihood weighed conditional least squares estimator |
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