论文标题
关于平均绝对偏差的使用：形状探索和分布函数估计
On Uses of Mean Absolute Deviation: Shape Exploring and Distribution Function Estimation
论文作者
论文摘要
平均绝对偏差函数用于以图形方式探索数据的模式和分布，以使分析师能够获得对原始数据的更多了解，并快速地培养对数据的深入了解，作为成功数据分析的重要基础。此外，提出了基于平均绝对偏差函数估算累积分布函数的新的非参数方法。这些新方法旨在成为一种一般的非参数类，其中包括经验分布函数作为特殊情况。仿真研究表明，理查森外推方法在平均平方误差方面在经典的经验估计器中取得了重大改进，并且与平滑的方法（例如立方样条和实际上小样品的线性样条）具有可比的结果。研究了所提出的估计器的性能。此外，理查森方法申请了实际数据应用，并用于估计危险浓度5％。
Mean absolute deviation function is used to explore the pattern and the distribution of the data graphically to enable analysts gaining greater understanding of raw data and to foster quick and a deep understanding of the data as an important fundament for successful data analytic. Furthermore, new nonparametric approaches for estimating the cumulative distribution function based on the mean absolute deviation function are proposed. These new approaches are meant to be a general nonparametric class that includes the empirical distribution function as a special case. Simulation study reveals that the Richardson extrapolation approach has a major improvement in terms of average squared errors over the classical empirical estimators and has comparable results with smooth approaches such as cubic spline and constrained linear spline for practically small samples. The properties of the proposed estimators are studied. Moreover, the Richardson approach applied for real data application and used to estimate the hazardous concentration five percent.
