A Density-Quantile Function Perspective on Robust Estimation.
STATE UNIV OF NEW YORK AT BUFFALO AMHERST STATISTICAL SCIENCE DIV
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This paper provides an overview to a new general approach to statistical data analysis and parameter estimation which could be called the quantile function approach. The aims of descriptive statistics to graphically summarize and display the data are obtained by Quantile-Box plots of the sample quantile function. The aims of goodness of fit are obtained by fitting smooth quantile functions to the sample quantile function. The aims of parameter estimation, especially robust estimation of location and scale parameters, are attained by regression analysis of the sample quantile function. The goal of a statistician in analyzing a batch of data X1,...,Xn should be both estimation of parameters and goodness of fit. By goodness of fit is meant fitting of the observed sample probabilities by a smooth probability law.
- Statistics and Probability