ON SCALE-INVARIANT M-STATISTICS IN MULTIVARIATE K SAMPLES
ON SCALE-INVARIANT M-STATISTICS IN MULTIVARIATE K SAMPLES
复制标题
多变量 K 样本中尺度不变的 M 统计量
DOI：
10.14490/jjss1995.26.241
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
T. Shiraishi
中科院分区：
文献类型：
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作者：
T. Shiraishi
提出了基于M统计量的尺度不变检验方法，用于检验多变量k样本模型的均匀性。在不假设Fisher相合性的条件下，给出了位置选择序列的渐近非中心X2分布，并得到了渐近鲁棒性.基于建议的M-检验统计量的排列测试被认为是。使用Monte Carlo模拟，这些测试的功率进行比较，置换测试的基础上参数检验统计。其次，基于尺度不变M-统计量，提出了位置参数的稳健估计，并给出了这些估计的渐近正态性。在研究了一种简单算法后，通过仿真艾德了M-估计量和最小二乘估计量的风险。对于单变量情形，我们发现：（i）所提出的M-方法相对于参数方法的渐近相对效率（ARE）与Huber（1964）所提出的单样本M-估计相对于样本均值的ARE一致;（ii）对于小样本情形，M-方法比参数方法更有效，但在基本分布为正态分布的情形除外。
Scale invariant tests based on M-statistics are proposed in order to test homogeneity in a multivariate k samp1e mode1. Asymptotic noncentral X2distributions are drawn under a contiguous sequence of location-alternatives without assuming Fisher consistency, and asymptotic robustness is derived . Permutation tests based on the proposed M-test statistics are considered . Using a Monte Carlo simulation, the power of these tests is compared with permutation tests based on parametric test statistics. Next, robust estimators for location parameters are proposed, based on sca1e-invariant M-statistics, and the asymptotic normality of these estimators is drawn. After a simple algorithm is studied, the risks of the M-estimators and the least squares estimators are compar ed in a simulation. For the univariate case, it is found that(i)the asymptotic relative efficiency(ARE)of the proposed M-procedures relative to parametric procedures agrees with the ARE of one-sample M-estimator proposed by Huber (1964)relative to the sample mean, and that(ii)for small sample sizes, the M-procedures are more efficient than parametric procedures except for the case where the underlying distribution is normal.