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http://dx.doi.org/10.5351/KJAS.2017.30.4.579

Multivariate empirical distribution plot and goodness-of-fit test  

Hong, Chong Sun (Department of Statistics, Sungkyunkwan University)
Park, Yongho (Department of Statistics, Sungkyunkwan University)
Park, Jun (Department of Statistics, Sungkyunkwan University)
Publication Information
The Korean Journal of Applied Statistics / v.30, no.4, 2017 , pp. 579-590 More about this Journal
Abstract
The multivariate empirical distribution function could be defined when its distribution function can be estimated. It is known that bivariate empirical distribution functions could be visualized by using Step plot and Quantile plot. In this paper, the multivariate empirical distribution plot is proposed to represent the multivariate empirical distribution function on the unit square. Based on many kinds of empirical distribution plots corresponding to various multivariate normal distributions and other specific distributions, it is found that the empirical distribution plot also depends sensitively on its distribution function and correlation coefficients. Hence, we could suggest five goodness-of-fit test statistics. These critical values are obtained by Monte Carlo simulation. We explore that these critical values are not much different from those in text books. Therefore, we may conclude that the proposed test statistics in this work would be used with known critical values with ease.
Keywords
Empirical distribution plot; Quantile vector; normal mixture;
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Times Cited By KSCI : 4  (Citation Analysis)
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