Multivariate statistical theory based on robust statistics

提出了基于学院化稳健统计量的双向交互布局中位置参数的统计估计方法。研究了当单元大小趋于无穷大时，其过程的大样本性质。虽然在M-估计理论中假设了Fisher相合性，但本文并不需要。通过仿真研究可以看出，除了基础分布为正态分布的情况外，所提出的估计器比最小二乘估计器更有效。在单样本和双样本模型中，给出了位置参数的渐近可信区间。这些都是基于尺度不变M统计量的健壮程序。单样本程序具有与Huber的M-估计量相同的稳健性。在我的书《Tokei Kagaku》中，讨论了参数参数、非参数参数和半参数参数。通过对非正态分布和拟合优度检验的搜索，给出了三种方法的选择方法。

Statistical estimation procedures are proposed based on studentized robust statistics for location parameters in two-way layouts with interaction. Large sample properties of their procedures as the cell size tends to infinity are investigated. Although Fisher's consistency is assumed in the theory of M-estimators, it is not needed in this paper. By simulation studies, it can be seen that the proposed estimators are more efficient than least squares estimators except for the case where the underlying distribution is normal.Asymptotic confidence intervals of location parameters are proposed in one-and two-sample models. These are robust procedures based on scale-invariant M-statistics. The one-sample procedures have the same robustness as Huber's M-estimators. The asymptotic efficiency of the proposed confidence intervals is given by a numerical integration.In my book entitled "Tokei Kagaku", parametorics, nonparametorics and semiparametorics are discussed. The way of making a selection from the three procedures is stated based on the search of the undelying distribution and goodness of fit tests.