Parker, Thomas (2010): A comparison of alternative approaches to supnorm goodness of git gests with estimated parameters.
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Abstract
Goodness of fit tests based on supnorm statistics of empirical processes have nonstandard limit ing distributions when the null hypothesis is composite — that is, when parameters of the null model are estimated. Several solutions to this problem have been suggested, including the calculation of adjusted critical values for these nonstandard distributions and the transformation of the empirical process such that statistics based on the transformed process are asymptotically distributionfree. The approximation methods proposed by Durbin (1985) can be applied to compute appropriate critical values for tests based on supnorm statistics. The resulting tests have quite accurate size, a fact which has gone unrecognized in the econometrics literature. Some justification for this accuracy lies in the similar features that Durbin’s approximation methods share with the theory of extrema for Gaussian random fields and for GaussMarkov processes. These adjustment techniques are also related to the transformation methodology proposed by Khmaladze (1981) through the score func tion of the parametric model. Monte Carlo experiments suggest that these two testing strategies are roughly comparable to one another and more powerful than a simple bootstrap procedure.
Item Type:  MPRA Paper 

Original Title:  A comparison of alternative approaches to supnorm goodness of git gests with estimated parameters 
Language:  English 
Keywords:  Goodness of fit test; Estimated parameters; Gaussian process; GaussMarkov process; Boundary crossing probability; Martingale transformation 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C14  Semiparametric and Nonparametric Methods: General C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C12  Hypothesis Testing: General C  Mathematical and Quantitative Methods > C4  Econometric and Statistical Methods: Special Topics > C46  Specific Distributions ; Specific Statistics 
Item ID:  22926 
Depositing User:  Thomas Parker 
Date Deposited:  28 May 2010 09:36 
Last Modified:  28 Sep 2016 19:02 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/22926 
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