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一般线性回归中部分参数假设的秩检验
This paper considers the general linear regression model $Y_i = \sum_j \beta_j x_{ij} + \varepsilon_i$, and studies the problem of testing hypotheses about some of the $\beta$'s while regarding others as nuisance parameters. The test criteria discussed, which are based on ranks of residuals, are shown to be asymptotically distribution-free.
用秩检验多条回归直线是否重合
For several linear regression lines $Y_{ij} = \alpha_i + \beta_i(x_{ij} - x{_i.}) + Z_{ij}, i = 1,\cdots, k; j = 1, \cdot, n_i$, a statistic for testing $\alpha_i = \alpha, \beta_i = \beta$ is constructed based on the simultaneous ranking of all the observations. The asymptotic properties of the criterion are also studied. The results are, however, not directly applicable to the general design model $Y_{ij} = \alpha_i + \beta_i x_{ij} + Z_{ij}$, unless it is assumed that the…
多个回归参数的秩得分比较
For testing $\beta_i = \beta, i = 1,\cdots, k$, in the model $Y_{ij} = \alpha + \beta_iX_{ij} + Z_{ij} j = 1,\cdots, n_i$ a class of rank score tests is presented. The test statistic is based on the simultaneous ranking of all the observations in the different $k$ samples. Its asymptotic distribution is proved to be chi square under the hypothesis and noncentral chi square under an appropriate sequence of alternatives. The asymptotic efficiency of the given procedure…