Representative Points of Univariate Distribution in Statistical Simulation

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  Representative Points (RP) have been considered by many people. It is a set of points that can retain majority of information about the population. Traditional Monte Carlo, Bootstrap and Resampling are the basic methods in statistical simulation based on a random sample. Fang et al. (2013) pointed out firstly that we can use RP to replace i.i.d. random samples, to construct an approximate distribution and then resample from the approximation for Statistical inference. In this talk, we consider the univariate distribution (the students distribution), and indicate that using this new method to do the statistical simulation, such as point estimation of parameters (mean, variance, skewness and kurtosis), estimation of density function and quantiles, can significantly improve the accuracy of the estimator of the statistics, and accelerate the converging speed of the statistics. This is a joint work with Kai-Tai Fang and Wen-Jun Wang. This work is partially supported by UIC research grant No.R201409.
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