Abstract
By means of the Poisson type representation of multivariate empirical processes and using a generalization of the Birnbaum Marshall inequality it is shown that the empirical process converges in distribution even when it is weighted by some unbounded weighting functions.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Bickel, P.J., Wichura, M.J. (1971) Convergence criteria for multiparameter stochastic processes and some applications. Ann. Math. Statist. 42, 1656–1670.
Chibisov, D.M. (1965) An investigation of the asymptotic power of tests of fit. Theor. Prob. and Appl. 10, 421–437.
Govindarajulu, Z., Le Cam, L., Raghavachari, M. (1967) Generalizations of theorems of Chernoff-Savage on asymptotic normality of nonparametric test statistics. Proc. of Fifth Berkeley Symp. on Math. Statist. and Prob. 609–638, Univ. of Calif. Press.
Kac, M. (1949) On deviations between theoretical and empirical distributions. Proc. Nat. Acad. Sci. 35, 252–257.
Neuhaus, G. (1971) On weak convergence of stochastic processes with multidimensional time parameter. Ann. Math. Statist. 42, 1285–1295.
Pyke, R., Shorack, G.R. (1968) Weak convergence of a two-sample empirical process and a new approach to Chernoff-Savage Theorems. Ann. Math. Statist. 39, 755–771.
Rosenblatt, M. (1975) A quadratic measure of deviation of two-dimensional density estimates and a test of independence. Ann. Statist. 3, 1–14.
Rüschendorf, L. (1976) Asymptotic distributions of multivariate rank order statistics. Ann. Statist. 3, 912–923.
Wichura, M. (1973) Some Strassen-type laws of the iterated logarithm for multi-parameter stochastic processes with independent increments. Ann. Probab. 1, 272–296.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1980 Springer-Verlag
About this paper
Cite this paper
Rüschendorf, L. (1980). Weak convergence of the weighted multiparameter empirical process. In: Raoult, JP. (eds) Statistique non Paramétrique Asymptotique. Lecture Notes in Mathematics, vol 821. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0097425
Download citation
DOI: https://doi.org/10.1007/BFb0097425
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-10239-7
Online ISBN: 978-3-540-38318-5
eBook Packages: Springer Book Archive
