scholarly journals On goodness-of-fit tests for parametric hypotheses in perturbed dynamical systems using a minimum distance estimator

2016 ◽  
Vol 19 (3) ◽  
pp. 259-287 ◽  
Author(s):  
Maroua Ben Abdeddaiem
Keyword(s):  
Dynamical Systems ◽  
Minimum Distance ◽  
Goodness Of Fit ◽  
Goodness Of Fit Tests ◽  
Minimum Distance Estimator ◽  
Distance Estimator

scholarly journals Asymptotic Distribution of Cramer-von Mises Statistic When Contamination Exists

2015 ◽  
Vol 5 (1) ◽  
pp. 90
Author(s):  
Mayumi Naka ◽  
Ritei Shibata
Keyword(s):  
Maximum Likelihood ◽  
Asymptotic Distribution ◽  
Minimum Distance ◽  
Goodness Of Fit ◽  
Likelihood Estimator ◽  
Goodness Of Fit Test ◽  
Minimum Distance Estimator ◽  
Von Mises Statistic ◽  
Von Mises ◽  
Distance Estimator

In this paper, asymptotic distribution of Cram\'er-von Mises goodness-of-fit test statistic is investigated when contamination exists.<br />We first derive the asymptotic distribution of the Cram\'er-von Mises statistic when the observations are contaminated with noise as a mixture.<br />The result is extended to the case where the parameters are estimated by the minimum distance estimator,<br />which minimizes the Cram\'er-von Mises statistic.<br />In both cases the asymptotic distribution of the Cram\'er-von Mises statistic is given by that of the weighted infinite sum of non-central $\chi^2_1$ variables and the effect of contamination appears only in the non-centrality of the variables.<br />We also demonstrate the robustness of the goodness-of-fit test by Monte Carlo simulations when the parameters are estimated<br />by the minimum distance estimator and the maximum likelihood estimator.<br />Numerical experiments indicate that the use of the minimum distance estimator makes the test insensitive to contamination whereas the power is retained almost the same as that of the maximum likelihood estimator.

New Goodness-of-Fit Tests for Pareto Distributions

2009 ◽  
Vol 39 (2) ◽  
pp. 691-715 ◽  
Author(s):  
Maria L. Rizzo
Keyword(s):  
Goodness Of Fit ◽  
Test Statistics ◽  
New Approach ◽  
Goodness Of Fit Tests ◽  
Pareto Distributions ◽  
Heavy Tailed Distributions ◽  
The Family ◽  
Euclidean Distances ◽  
Heavy Tailed ◽  
Distance Estimator

AbstractA new approach to goodness-of-fit for Pareto distributions is introduced. Based on Euclidean distances between sample elements, the family of statistics and tests is indexed by an exponent in (0,2) on Euclidean distance. The corresponding tests are statistically consistent and have excellent performance when applied to heavy-tailed distributions. The exponent can be tailored to the particular Pareto distribution. The goodness-of-fit statistic measures all types of differences between distributions, hence it is also applicable as a minimum distance estimator. Implementation of the test statistics is developed and applied to estimation of the tail index in three well known examples of claims data, and compared with the classical EDF statistics.

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