用最小绝对偏差方法(LAD)估计极值分布参数的探讨  

REGRESSIVE PARAMETER-ESTIMATING WITH LEAST ABSOLUTE DEVIATION IN EXTREME VALUE DISTRIBUTION

作　　者：吴香华[1] 秦伟良[2] 王新蕾[1] 俞书平[1] 

机构地区：[1]南京信息工程大学数学系,南京210044 [2]东南大学经管学院,南京210096

出　　处：《气象科学》2006年第3期260-264,共5页Journal of the Meteorological Sciences

基　　金：国家自然科学基金项目(编号:70301010)资助

摘　　要：数理统计问题中的最小绝对偏差方法(Least Absolute Deviation)由于具有良好的稳健性,近年来备受重视。本文所研究的是如何将最小绝对偏差法及非线性回归模型相结合,应用于极值分布的参数估计,并与经典的参数估计法相比较。通过对徐州市降雨量数据的研究表明,改进后的参数估计法不仅提高了模型拟和的精确度,而且有良好的稳定性,可以推广到相关气象要素的预测、预报研究中。其中,将LAD法运用于极值分布模型是一个新的尝试。Least Absolute Deviation substituting Least Squares Method is introduced to establish the aim function ∑i=1^n｜y^（i）-f（xi ,β）｜ in the estimation of position, scale and shape parameters in the extreme value distribution. The extreme value in the stochastic process is the maximum or minimum value on a given time trial, so the extreme method emphasizes particularly the tail of a distribution instead of the whole, which makes sense to forecast the disasters, reduce or avoid losses and so on. As one of the most important step, parameter-estimating attracts more and more consideration. Compared with the classical estimation, the new method using LAD and nonlinear regression model improves in many aspects. It has been found that LAD can enhance not only the accuracy of the forecast but also the calculation stability.

关 键 词：极值分布 LAD法 年最大日降雨量 Kolmogorov检验 

分 类 号：P413[天文地球—大气科学及气象学]