A comparison of alternative approaches to sup-norm goodness of fit tests with estimated parameters

Parker, Thomas M.

doi:10.1920/wp.cem.2010.3410

Cited by 1 publication

(1 citation statement)

References 42 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the same context, Durbin (1973Durbin ( , 1975 investigated several approaches to compute approximate critical values for the Kolmogorov-Smirnov statistic. The martingale transform of Khmaladze (1981) and Durbin (1975)'s approach based on approximate boundary crossing probabilities are reviewed and compared in Parker (2010) when M is a locationscale or a scale-shape univariate family. For tests based on the Cramér-von Mises, the Anderson-Darling or the Watson statistics, Stephens (1976) (see also Sukhatme, 1972;Stephens, 1974) used the fact that the asymptotic distributions of these statistics can be expressed as a weighted sum of χ 2 1 variables and explained in detail how to compute the unknown weights when M is the univariate normal or the exponential distribution.…”

Section: Introductionmentioning

confidence: 99%

Goodness‐of‐fit testing based on a weighted bootstrap: A fast large‐sample alternative to the parametric bootstrap

Kojadinovic

Yan

2012

Can J Statistics

View full text Add to dashboard Cite

The process comparing the empirical cumulative distribution function of the sample with a parametric estimate of the cumulative distribution function is known as the empirical process with estimated parameters and has been extensively employed in the literature for goodness‐of‐fit testing. The simplest way to carry out such goodness‐of‐fit tests, especially in a multivariate setting, is to use a parametric bootstrap. Although very easy to implement, the parametric bootstrap can become very computationally expensive as the sample size, the number of parameters, or the dimension of the data increase. An alternative resampling technique based on a fast weighted bootstrap is proposed in this paper, and is studied both theoretically and empirically. The outcome of this work is a generic and computationally efficient multiplier goodness‐of‐fit procedure that can be used as a large‐sample alternative to the parametric bootstrap. In order to approximately determine how large the sample size needs to be for the parametric and weighted bootstraps to have roughly equivalent powers, extensive Monte Carlo experiments are carried out in dimension one, two and three, and for models containing up to nine parameters. The computational gains resulting from the use of the proposed multiplier goodness‐of‐fit procedure are illustrated on trivariate financial data. A by‐product of this work is a fast large‐sample goodness‐of‐fit procedure for the bivariate and trivariate t distribution whose degrees of freedom are fixed. The Canadian Journal of Statistics 40: 480–500; 2012 © 2012 Statistical Society of Canada

show abstract