A goodness-of-fit test based on Kendall’s process: Durante's bivariate copula models

2021 ◽  
Vol 16 (3) ◽  
pp. 2851-2882
Author(s):  
N'dri Hubert Bian
Keyword(s):  
Goodness Of Fit ◽  
Empirical Process ◽  
Bootstrap Method ◽  
Parametric Bootstrap ◽  
Goodness Of Fit Test ◽  
Copula Models ◽  
Testing Procedures ◽  
Fitting Procedure ◽  
Fit Testing ◽  
Von Mises

The proposed goodness-of-fit testing procedures for copula models are fairly recent. The new test statistics or omnibus tests are functional of an empirical process motivated by the theoretical and empirical versions of Kendall’s or Spearman's dependence function. In this paper, we propose a fitting procedure for a symmetric and flexible copula model with a non-zero singular component using the Kendall process. The conditions under which this empirical process weakly converges are satisfied. Using a parametric bootstrap method that allows to compute approximate p-values, it is empirically shown that tests based on the Cramer-von Mises distance keeps the prescribed value for the nominal level under the null hypothesis. Simulation studies that demonstrate the power of the fit test are presented.

scholarly journals Raking-ratio empirical process with auxiliary information learning

2020 ◽  
Vol 24 ◽  
pp. 435-453
Author(s):  
Mickael Albertus
Keyword(s):  
Asymptotic Behavior ◽  
Goodness Of Fit ◽  
Empirical Process ◽  
Information Source ◽  
Auxiliary Information ◽  
Computational Method ◽  
Empirical Measure ◽  
Ratio Method ◽  
Goodness Of Fit Test ◽  
Chi Square

The raking-ratio method is a statistical and computational method which adjusts the empirical measure to match the true probability of sets of a finite partition. The asymptotic behavior of the raking-ratio empirical process indexed by a class of functions is studied when the auxiliary information is given by estimates. These estimates are supposed to result from the learning of the probability of sets of partitions from another sample larger than the sample of the statistician, as in the case of two-stage sampling surveys. Under some metric entropy hypothesis and conditions on the size of the information source sample, the strong approximation of this process and in particular the weak convergence are established. Under these conditions, the asymptotic behavior of the new process is the same as the classical raking-ratio empirical process. Some possible statistical applications of these results are also given, like the strengthening of the Z-test and the chi-square goodness of fit test.

scholarly journals Testing in Nonparametric Accelerated Life Time Models

2016 ◽  
Vol 37 (1) ◽  
Author(s):  
Hannelore Liero
Keyword(s):  
Limit Distribution ◽  
Goodness Of Fit ◽  
Bootstrap Method ◽  
Life Time ◽  
Test Statistic ◽  
Goodness Of Fit Test ◽  
Time Model ◽  
Power Of The Test ◽  
Accelerated Life ◽  
Type Test

A goodness-of-fit test for testing the acceleration function in a nonparametric life time model is proposed. For this aim the limit distribution of an L2-type test statistic is derived. Furthermore, a bootstrap method is considered and the power of the test is studied.

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.

scholarly journals Goodness of Fit Tests for Marshal-Olkin Extended Rayleigh Distribution

2019 ◽  
pp. 587-598
Author(s):  
Naz Saud ◽  
Sohail Chand
Keyword(s):  
Goodness Of Fit ◽  
Empirical Distribution ◽  
Rayleigh Distribution ◽  
Test Statistic ◽  
Goodness Of Fit Test ◽  
Goodness Of Fit Tests ◽  
Estimated Parameters ◽  
Percentage Points ◽  
Anderson Darling ◽  
Von Mises

A class of goodness of fit tests for Marshal-Olkin Extended Rayleigh distribution with estimated parameters is proposed. The tests are based on the empirical distribution function. For determination of asymptotic percentage points, Kolomogorov-Sminrov, Cramer-von-Mises, Anderson-Darling,Watson, and Liao-Shimokawa test statistic are used. This article uses Monte Carlo simulations to obtain asymptotic percentage points for Marshal-Olkin extended Rayleigh distribution. Moreover, power of the goodness of fit test statistics is investigated for this lifetime model against several alternatives.

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