地震前兆数据的稳健回归与建模

基于正态密度ψ函数的M 估计,建立了含有趋势和周期项组合的稳健回归数学模型,对含有离群值的仿真数据进行了最小二乘估计、稳健估计和修正离群值后的最小二乘估计.结果表明稳健估计可以克服最小二乘估计受离群值影响较大的弊病,模型参数更接近实际.对地倾斜和地下气体等前兆观测数据的实际算例表明,用稳健回归方法建立的数学模型避免了少数离群值的干扰影响,更加真实地反映了前兆观测数据的变化趋势,是前兆数据趋势变化分析的强有力的数学工具.

THE ROBUST REGRESSION METHOD AND MODEL USED IN EARTHQUAKE PRECURSOR DATA PROCESSING

Based on the M-estimation of normal density ψfunction, a robust regression mathematical model that contains the combination of tendency term and periodic term is set up. The emulation data that contains a few discrete points are calculated by using three methods (least-squares estimation, robust estimation, least-squares estimation after revising the discrete points). It is shown that robust estimation can avoid the evil of least-square method in which the result will be considerably influenced by discrete points, and the mathematical model parameter is closer to the fact. The calculation results of precursor data (tide of the solid earth and underground gas) also show that this mathematical model can avoid the disturbance of the discrete points and more truly reflect the tendency of precursor data. The method will become a powerful tool for analysing the tendency of precursor data.