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Goodnes-of-fit tests for location and scale families based on a weighted L$_{2}$-Wasserstein distance measure

Content Provider	Springer Nature Link
Author	Wet, T.
Copyright Year	2002
Abstract	In two recent papers del Barrio et al. (1999) and del Barrio et al. (2000) consider a new class of goodness-of-fit statistics based on theL $_{2}$-Wasserstein distance. They derive the limiting distribution of these statistics and show that the normal distribution is the only location-scale family for which this limiting distribution has the “loss of degrees of freedom” property, due to the estimation of the unknown parameters. In this paper a weightedL $_{2}$-Wasserstein distance is considered and it is proven that these statistics retain the loss of degrees of freedom property for general classes of distributions if applied separately to the location family and to the scale family and if the “right” weight function is used. These weight functions are such that the corresponding minimum distance estimators for the location parameter and the scale parameter are asymptotically efficient. Examples are discussed for both location and scale families.
Starting Page	89
Ending Page	107
Page Count	19
File Format	PDF
ISSN	11330686
Journal	Test
Volume Number	11
Issue Number	1
e-ISSN	18638260
Language	English
Publisher	Springer-Verlag
Publisher Date	2002-01-01
Publisher Institution	Spanish Society of Statistics and Operations Research
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	goodness-of-fit Wasserstein distance location family scale family quantile process Brownian bridge minimum distance estimation limiting distributions asymptotic efficiency Karhunen-Loève expansion sum of weighted chisquares loss of degrees of freedom Asymptotic properties of tests Asymptotic distribution theory Gaussian processes Statistics Statistical Theory and Methods Statistics for Business/Economics/Mathematical Finance/Insurance
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Statistics, Probability and Uncertainty

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