Distribution results for distance functions based on the modified empirical distribution function of M. Kac

1972 ◽  
Vol 24 (1) ◽  
pp. 101-110 ◽  
Author(s):  
Miklós Csörgő
Keyword(s):  
Distribution Function ◽  
Empirical Distribution Function ◽  
Empirical Distribution ◽  
Distance Functions

Projection Pursuit Indices Based on the Empirical Distribution Function

2005 ◽  
Vol 14 (3) ◽  
pp. 700-715 ◽  
Author(s):  
Igor Perisic ◽  
Christian Posse
Keyword(s):  
Distribution Function ◽  
Empirical Distribution Function ◽  
Empirical Distribution ◽  
Projection Pursuit

New goodness-of-fit tests based on fiducial empirical distribution function

2009 ◽  
Vol 53 (4) ◽  
pp. 1132-1141 ◽  
Author(s):  
Xingzhong Xu ◽  
Xiaobo Ding ◽  
Shuran Zhao
Keyword(s):  
Distribution Function ◽  
Goodness Of Fit ◽  
Empirical Distribution Function ◽  
Empirical Distribution ◽  
Goodness Of Fit Tests

scholarly journals Nonparametric Estimation of Multivariate Extreme Value Copulas with Known and Unknown Marginal Distributions

2021 ◽  
Vol 2068 (1) ◽  
pp. 012003
Author(s):  
Ayari Samia ◽  
Mohamed Boutahar
Keyword(s):  
Distribution Function ◽  
Empirical Distribution Function ◽  
Extreme Values ◽  
Empirical Distribution ◽  
Extreme Value ◽  
Dependence Function ◽  
Marginal Distributions ◽  
Nonparametric Estimators ◽  
Monte Carlo Experiments ◽  
Multivariate Extreme Values

Abstract The purpose of this paper is estimating the dependence function of multivariate extreme values copulas. Different nonparametric estimators are developed in the literature assuming that marginal distributions are known. However, this assumption is unrealistic in practice. To overcome the drawbacks of these estimators, we substituted the extreme value marginal distribution by the empirical distribution function. Monte Carlo experiments are carried out to compare the performance of the Pickands, Deheuvels, Hall-Tajvidi, Zhang and Gudendorf-Segers estimators. Empirical results showed that the empirical distribution function improved the estimators’ performance for different sample sizes.

Semiparametric estimation and inference

2019 ◽  
pp. 139-164
Author(s):  
M. D. Edge
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Empirical Distribution Function ◽  
Empirical Distribution ◽  
Permutation Test ◽  
Cumulative Distribution ◽  
Permutation Testing ◽  
Unknown Distribution ◽  
Regression Parameters ◽  
Independent Observations

Nonparametric and semiparametric statistical methods assume models whose properties cannot be described by a finite number of parameters. For example, a linear regression model that assumes that the disturbances are independent draws from an unknown distribution is semiparametric—it includes the intercept and slope as regression parameters but has a nonparametric part, the unknown distribution of the disturbances. Nonparametric and semiparametric methods focus on the empirical distribution function, which, assuming that the data are really independent observations from the same distribution, is a consistent estimator of the true cumulative distribution function. In this chapter, with plug-in estimation and the method of moments, functionals or parameters are estimated by treating the empirical distribution function as if it were the true cumulative distribution function. Such estimators are consistent. To understand the variation of point estimates, bootstrapping is used to resample from the empirical distribution function. For hypothesis testing, one can either use a bootstrap-based confidence interval or conduct a permutation test, which can be designed to test null hypotheses of independence or exchangeability. Resampling methods—including bootstrapping and permutation testing—are flexible and easy to implement with a little programming expertise.

The realized empirical distribution function of stochastic variance with application to goodness-of-fit testing

2019 ◽  
Vol 212 (2) ◽  
pp. 556-583 ◽  
Author(s):  
Kim Christensen ◽  
Martin Thyrsgaard ◽  
Bezirgen Veliyev
Keyword(s):  
Distribution Function ◽  
Goodness Of Fit ◽  
Empirical Distribution Function ◽  
Empirical Distribution ◽  
Goodness Of Fit Testing ◽  
Fit Testing
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