周世健. 方差的边缘极大似然估计[J]. 武汉大学学报 ( 信息科学版), 1993, 18(2): 48-54.
引用本文: 周世健. 方差的边缘极大似然估计[J]. 武汉大学学报 ( 信息科学版), 1993, 18(2): 48-54.
Zhou Shijian. The Marginal Maximum Likelihood Estimate of Variance[J]. Geomatics and Information Science of Wuhan University, 1993, 18(2): 48-54.
Citation: Zhou Shijian. The Marginal Maximum Likelihood Estimate of Variance[J]. Geomatics and Information Science of Wuhan University, 1993, 18(2): 48-54.

方差的边缘极大似然估计

The Marginal Maximum Likelihood Estimate of Variance

  • 摘要: 测量平差问题中,方差估计理论是复杂的。本文基于概括模型,组成自由项f(极大似然估计MLE)的密度函数和改正数向量V的线性函数(边缘极大似然估计MMLE)的密度函数,详细推导了函数模型与随机模型中,未知参数X与σ02的似然估计公式,分析了基于两种密度函数所得σ02的似然估计存在差异的真正原因,并对两种方法所得的σ02和X的统计性质进行了讨论。指出边缘极大似然估计,σ02的具有良好的统计性质,可改善极大似然估计σ02的不定性(有偏);并且对任一平差模型的边缘极大似然估计,σ02无偏、有效的统计性质是一致的。

     

    Abstract: The paper based on general model, costructed density function of free term f (Maximum Likelihood Estimate) and function of residual vector V (Marginal Maximum Likelihood Estimate),the estimate formulae of unit weighted variance are derived in detail, their statistcs properties are discussed,the key factors of unequal between two estimates are analysed,pointed out the basic principle of the MML estimate which can improve the statis-tics property of estimation, the MML estimate of variance is unbiased,efficiency to arbitrary adjustment model.

     

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