本文選題：多元方差分析 + wilks檢驗(yàn)統(tǒng)計(jì)量��； 參考：《蘭州財(cái)經(jīng)大學(xué)》2017年碩士論文

【摘要】：多元方差分析是一種非常重要的多元統(tǒng)計(jì)分析方法,主要任務(wù)包括:檢驗(yàn)各個(gè)因素對(duì)實(shí)驗(yàn)指標(biāo)的影響是否顯著、估計(jì)出各個(gè)因子不同水平的效應(yīng)值、估計(jì)出各個(gè)因子水平之間的交互效應(yīng)值、估計(jì)出協(xié)方差陣等等。其中首要任務(wù)是檢驗(yàn)各個(gè)因素對(duì)實(shí)驗(yàn)指標(biāo)的影響是否顯著。為此,需要進(jìn)行假設(shè)檢驗(yàn),較常使用的檢驗(yàn)統(tǒng)計(jì)量有:wilks檢驗(yàn)統(tǒng)計(jì)量、Hotelling跡檢驗(yàn)統(tǒng)計(jì)量、Pillai-Bartlett準(zhǔn)則檢驗(yàn)統(tǒng)計(jì)量以及Roy最大特征值檢驗(yàn)統(tǒng)計(jì)量。這些檢驗(yàn)統(tǒng)計(jì)量經(jīng)過適當(dāng)變形,可以轉(zhuǎn)化為服從F分布的檢驗(yàn)統(tǒng)計(jì)量。這些檢驗(yàn)統(tǒng)計(jì)量的導(dǎo)出過程計(jì)算量較大,將它們轉(zhuǎn)化為服從F分布檢驗(yàn)統(tǒng)計(jì)量的推導(dǎo)證明過程較難理解,需要用到高深的數(shù)理統(tǒng)計(jì)知識(shí)。為了克服上述問題,可以利用投影技術(shù)將高維數(shù)據(jù)降低為一維數(shù)據(jù),能夠證明投影后的數(shù)據(jù)仍然滿足同方差且服從正態(tài)分布,可以直接基于線性變換后的數(shù)據(jù)構(gòu)建F分布檢驗(yàn)統(tǒng)計(jì)量進(jìn)行多元方差分析,這種分析方法在很大程度上改進(jìn)了多元方差分析的效率�；舅悸窞�:該F檢驗(yàn)統(tǒng)計(jì)量與一般的F統(tǒng)計(jì)量有所不同,其中投影方向事先并不知道,所以無法計(jì)算出檢驗(yàn)統(tǒng)計(jì)量具體數(shù)值。投影技術(shù)可以使組間差異最大化,也可以使組間差異最小化,為了排除不同投影方向?qū)z驗(yàn)結(jié)果的干擾,可以向使組間差異最小化方向投影,然后計(jì)算F檢驗(yàn)統(tǒng)計(jì)量具體取值F_1,若該值落入拒絕域中,則向任何方向投影計(jì)算F檢驗(yàn)統(tǒng)計(jì)量具體取值均落入拒絕域,故各組樣本均值向量之間確實(shí)存在差異,依據(jù)小概率事件在一次實(shí)驗(yàn)中不發(fā)生原則,有充分理由拒絕原假設(shè);如果F_1沒有落入拒絕中,有可能向其他方向投影,計(jì)算的F檢驗(yàn)統(tǒng)計(jì)量具體取值落入拒絕域,為了排除這種情況,可以計(jì)算出F檢驗(yàn)統(tǒng)計(jì)量最大值F_2,若F統(tǒng)計(jì)量最大值仍然落入接受域,則向任何方向投影,計(jì)算F檢驗(yàn)統(tǒng)計(jì)量具體取值均落入接受域,即各組樣本的均值向量確實(shí)沒有差異,故不拒絕原假設(shè);如果F_1落入接受域,F_2落入拒絕域,則可以調(diào)整顯著性水平,直到出現(xiàn)F_1落入拒絕域或者F_2落入接受域。
[Abstract]:Multivariate variance analysis is a very important method of multivariate statistical analysis. The main tasks include: to test whether the influence of each factor on the experimental index is significant, and to estimate the effect value of each factor at different levels. We estimate the interaction effect between each factor level, covariance matrix and so on. The primary task is to test whether the influence of each factor on the experimental indicators is significant. For this reason, we need to carry out hypothesis test. The commonly used test statistics are the: Wilks test statistic / Hotelling trace test statistic and the Pillai-Bartlett criterion test statistic and the Roy maximum eigenvalue test statistic. These test statistics can be transformed into test statistics from F distribution after proper deformation. It is difficult to understand the derivation process of these test statistics, which is difficult to understand when they are converted into the derivation of F distribution test statistics, so it is necessary to use advanced mathematical and statistical knowledge. In order to overcome the above problems, the projection technique can be used to reduce the high-dimensional data to one-dimensional data, and it can be proved that the projected data still satisfy the same square difference and follow the normal distribution. It is possible to construct F distribution test statistics directly based on linear transformation data for multivariate ANOVA. This method improves the efficiency of multivariate ANOVA to a great extent. The basic idea is that the F test statistic is different from the general F statistic, and the projection direction is not known in advance, so the concrete value of the test statistic can not be calculated. Projection technique can maximize or minimize the differences between groups. In order to eliminate interference of different projection directions to test results, it can be projected to minimize the differences between groups. If the value falls into the rejection domain, then the concrete value of F test statistic falls into the rejection domain, so there is a difference between the mean vectors of the samples in each group, and if the value of F test statistic falls into the rejection domain, the value of F test statistic can be calculated in any direction. According to the principle that a small probability event does not occur in an experiment, there is good reason to reject the original hypothesis. If FSP _ 1 does not fall into the rejection, it is possible to project in other direction, and the calculated F-test statistic falls into the rejection domain. In order to eliminate this situation, we can calculate the maximum value of F test statistic F2s. If the maximum value of F test statistic still falls into the acceptance domain, then if the maximum F statistic still falls into the acceptance domain, then projection in any direction to calculate the specific value of the F test statistic will fall into the acceptance domain. That is, there is no difference in the mean vector of each sample, so we do not reject the original hypothesis. If FS-1 falls into the receptive domain and FSt2 falls into the rejection domain, the significant level can be adjusted until FSP 1 falls into the rejection domain or FStus fall into the receptive domain.
【學(xué)位授予單位】：蘭州財(cái)經(jīng)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O212.4

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本文編號(hào)：1778082