Wang & Wells ["J. Amer. Statist. Assoc." 95 (2000) 62] describe a non-parametric approach for checking whether the dependence structure of a random sample of censored bivariate data is appropriately modelled by a given family of Archimedean copulas. Their procedure is based on a truncated version of the Kendall process introduced by Genest & Rivest ["J. Amer. Statist. Assoc." 88 (1993) 1034] and later studied by Barbe "et al". ["J. Multivariate Anal." 58 (1996) 197]. Although Wang & Wells (2000) determine the asymptotic behaviour of their truncated process, their model selection method is based exclusively on the observed value of its "L"-super-2-norm. This paper shows how to compute asymptotic "p"-values for various goodness-of-fit test statistics based on a non-truncated version of Kendall's process. Conditions for weak convergence are met in the most common copula models, whether Archimedean or not. The empirical behaviour of the proposed goodness-of-fit tests is studied by simulation, and power comparisons are made with a test proposed by Shih ["Biometrika" 85 (1998) 189] for the gamma frailty family. Copyright 2006 Board of the Foundation of the Scandinavian Journal of Statistics..
Tests are proposed for the hypothesis that the underlying copula of a continuous random pair is symmetric. The procedures are based on Cramér-von Mises and Kolmogorov-Smirnov functionals of a rank-based empirical process whose largesample behaviour is obtained. The asymptotic validity of a re-sampling method to compute P values is also established. The technical arguments supporting the use of a Chi-squared test due to Jasson are also presented. A power study suggests that the proposed tests are more powerful than Jasson's procedure under many scenarios of copula asymmetry. The methods are illustrated on a nutrient data set.
Deheuvels [J. Multivariate Anal. 11 (1981) [102][103][104][105][106][107][108][109][110][111][112][113] and Genest and Rémillard [Test 13 (2004) 335-369] have shown that powerful rank tests of multivariate independence can be based on combinations of asymptotically independent Cramér-von Mises statistics derived from a Möbius decomposition of the empirical copula process. A result on the large-sample behavior of this process under contiguous sequences of alternatives is used here to give a representation of the limiting distribution of such test statistics and to compute their relative local asymptotic efficiency. Local power curves and asymptotic relative efficiencies are compared under familiar classes of copula alternatives.
International audienceThe nonparametric test for change-point detection proposed by Gombay and Horváth is revisited and extended in the broader setting of empirical process theory. The resulting testing procedure for potentially multivariate observations is based on a sequential generalization of the functional multiplier central limit theorem and on modifications of Gombay and Horváth's seminal approach that appears to improve the finite-sample behavior of the tests. A large number of candidate test statistics based on processes indexed by lower-left orthants and half-spaces are considered and their performance is studied through extensive Monte Carlo experiments involving univariate, bivariate and trivariate data sets. Finally, practical recommendations are provided and the tests are illustrated on trivariate hydrological data. © 2012 Elsevier Inc
International audienceThe sample properties of various inference procedures in Lombard's smooth-change model are studied in this work. In particular, the power of six test statistics for the detection of change-points in the mean and the variance of a series of independent observations is investigated under several alternatives. The robustness of the procedures under heterogeneity and serial dependence is considered as well. An investigation of the efficiency of an estimator of the change-points is also presented. Conditional on these estimated change-points, least squares estimators of the means in Lombard's model are derived and their efficiency is carefully studied. The procedures are illustrated on two environmental data sets, namely the annual volume of discharge from the Nile River and the annual temperature anomalies for the northern hemisphere. It will be seen that Lombard's model is flexible, that the test statistics of Lombard (1987) are powerful, and that the proposed estimators have nice properties; hence Lombard's model has a high potential for applications in the environmental sciences
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