数量化理论Ⅰ的稳健性处理及其在矿产定量预测中的应用

STABILITY CALCULATION OF NUMERIZATION THEORY I AND JTS APPLICATION IN THE QUANTITATIVE PROGNOSIS OF MINERAL RESOURCES

多元回归有两个缺陷:(1)自变量的限制条件过为苛刻;(2)稳健性差。这两个缺陷对矿产定量预测有极为不利的影响。为此,笔者应用现代统计学新成果——稳健性统计理论和数量化理论I进行了较系统地研究:选用残差余弦值和及残差绝对值和分别作为目标函数,首次提出了最小化残差余弦值和的数量化理论I和最小化残差绝对值和的稳健性数量化理论I,并给出相应的解法;通过对实际资料的处理、计算与结果的分析、对比,得出定量预测方法——最小化残差绝对值和数量化理论I稳键性好,预测效果最佳的结论。

The multivariate regression has two defects. One is the greatly restricted condition of free variables, the other is the poor stability, both of which are very disadvantageous in the quantitative prognosis of mineral resources. For this reason, the author uses the new achievements of the modern statistical theory-the stability statistic theory and numerization theory I to make a systematical study. The residual sum of cosine value and the residual sum of absolute value are chosen as the objective functions respectively, to put forward, for the first time, the numerization theory I of the minimization residual sum of cosine value and stability numerization theory I of the minimization residual sum of absolute value. The associated solutions are also given. The processing and calculation of the firsthand data as well as the analysis and correlation of the results, reveal that the numerization theory I of the minimization residual sum of absolute value has a better stability and a better effect.