统计预测中虚假因子的识别理论及其在预测实践当中的应用(二)——偶然性相关率概率定理和偶然性复相关的识别与过滤

从（0,1）型的完备随机因子群与预报量之间的等概率相关出发,我们导出了偶然性相关率概率定理,即:任一含有n个（0,1）型元素的预报量序列,它与含有n个（0,1）型元素的完备随机因子群之间具有偶然性相关率m/n二的概率P_w（m/n）=C_n~m/2~n。类似于“偶然性单相关的识别与过滤”一文中的做法,引进统计量 并用其对预报因子进行显著性检验。文中给出了实际应用时应当执行的步骤。 然后本文将变量型从（0,1）型推广到K级划分的情况,于是得到K级偶然相关率概率定理,即:任一含有n个k级划分元素的预报量序列,它与包含n个k级划分元素的完备随机因子群之间具有的偶然性相关率m/n的概率P_w（m/n,k）=（k-1）~（n-m）C_n~m/K~n。

DETECTION THEORY FOR SHAM PREDICTORS IN STATISTICAL PREDICTION AND ITS APPLICATIONS IN THE PRACTICE PART II: THEOREM OF PROBABILITY OF ACCIDENTAL MULTICORRELATION RATE AND RECOGNITION, FITLERING OF SUCH CORRELATION

Starting from the eguiprobability correlation of complete random(0,l) -type predictor group with a predictand we have derived the theorem of probability of accidental multicorrelation rate, it states as: For any predictand containing n of(0, 1 ) -type occurrences, if it correlates with complete random (0, 1 ) -type predictor group in correlation rate m/n, then the probabity Pw 2 ( m/n ) of the correlation rate equals C_n~m/ 2~n. Namely the formula is Pw_2 (m/n) =C_n~m/2~n As in the article entitled "recognition and filtering of accidental sindle correlation", we introduce the statistic and do significance test for these predictors. In this paper we also suggested an effective performance procedure for practical application in statistical prediction. It follows in the paper that we extended the variable type from (0, 1) -type to K-graded type, and so derived the theorem of probability of K -class accidental multicorrelation rate. It states as: For any predictand containing n of K-class occurrences, if it correlates with complete random K-graded predictor group in correlation rate m/n, then the probability Pwk(m/n, K ) of the correlation rate equals ( K-1)~(n-m)C_n~m/K~n Namely: Pwk ( m/n, K ) = ( K-1 )~(n-m)C_n~m/K~n