PARAMETER-ESTIMATION IN NON-GAUSSIAN NOISE
PARAMETER-ESTIMATION IN NON-GAUSSIAN NOISE
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DOI：
10.1111/j.1365-246x.1988.tb03433.x
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发表时间：
1988-07-01
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影响因子：
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通讯作者：
CONSTABLE, CG
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文献类型：
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作者：
CONSTABLE, CG
模型参数的最小二乘估计在地球物理中有着广泛的应用。如果数据误差是高斯的和独立的，则最小二乘估计将是最大似然(ML)估计，并且将是无偏的和最小方差的。然而，如果噪声不是高斯的，例如如果数据受到极端异常值的污染，最小二乘拟合将导致参数估计可能有偏差或严重不准确。当误差的概率分布已知时，使用最大似然法可以获得一致和有效的(最小方差)参数估计。在某些情况下，可以根据经验确定噪声的分布，并且在最大似然估计中使用所得到的分布。此处描述了执行此操作的过程。使用地磁观测数据的每小时值来说明该技术。这些数据集包含许多周期分量，其幅度和相位在地球物理上很有趣。记录中的地磁暴等现象使噪声分布具有长尾性、不对称性和随位置变化的特点。使用迭代过程，可以使用平滑样条线对这些分布的形式进行建模。对于这些数据，最大似然估计产生了与标准稳健和最小二乘程序截然不同的结果。该技术有可能广泛应用于涉及从非高斯噪声中恢复已知形式的信号的其他问题。
Least squares (LS) estimation of model parameters is widely used in geophysics. If the data errors are Gaussian and independent the LS estimators will be maximum likelihood (ML) estimators and will be unbiased and of minimum variance. However, if the noise is not Gaussian, e.g. if the data are contaminated by extreme outliers, LS fitting will result in parameter estimates which may be biased or grossly inaccurate. When the probability distribution of the errors is known it is possible, using the maximum likelihood method, to obtain consistent and efficient (minimum variance) estimates of parameters. In some cases the distribution of the noise may be determined empirically, and the resulting distribution used in the ML estimation. A procedure for doing this is described here. Hourly values of geomagnetic observatory data are used to illustrate the technique. These data sets contain a number of periodic components, whose amplitudes and phases are geophysically interesting. Geomagnetic storms and other phenomena in the record make the noise distribution long-tailed, asymmetric and variable with location. Using an iterative procedure, one can model the form of these distributions using smoothing splines. For these data ML estimation yields quite different results from standard robust and LS procedures. The technique has the potential for widespread application to other problems involving the recovery of a known form of signal from non-Gaussian noise.