Article PDF
Avoid common mistakes on your manuscript.
References
Berk, R.H.: Limiting behavior of posterior distribution when the model is incorrect. Ann. Math. Statist. 37, 51–58 (1966)
Billingsley, P.: Convergence of Probability Measures. New York: Wiley 1968
Blum, J.R., Kiefer, J., Rosenblatt, M.: Distribution-free tests of independence based on the sample distribution functions. Ann. Math. Statist. 32, 485–498 (1961)
Brown, B.M.: Martingale central limit theorems. Ann. Math. Statist. 42, 59–66 (1971)
Chow, Y.S., Robbins, H., Teicher, H.: Moments of randomly stopped sums. Ann. Math. Statist. 36, 789–799 (1964)
Darling, D.A., Robbins, H.: Some nonparametric sequential tests with power 1. Proc. Nat. Acad. Sci. 61, 804–809 (1968)
David, H.A.: Order Statistics. New York: Wiley 1970
Hájek, J.: Some extensions of the Wald-Wolfowitz-Noether theorem. Ann. Math. Statist. 32, 506–523 (1961)
Hájek, J., šidák, Z.: Theory of Rank Tests. New York: Academic Press 1967
Hoeffding, W.: A nonparametric test for independence. Ann. Math. Statist. 19, 546–557 (1948)
Hoeffding, W.: On the distribution of the expected values of the order statistics. Ann. Math. Statist. 24, 93–100 (1953)
Hoeffding, W.: On the centering of a simple linear rank statistic. Ann. Statist. 1, 54–66 (1973)
Kendall, M.G.: A new measure of rank correlation. Biometrika 30, 81–93 (1938)
Kiefer, J.: Skorohod embedding of multivariate rv's and the sample df. Z. Wahrscheinlichkeits-theorie verw. Gebiete 24, 1–35 (1972)
Lehmann, E.L.: Some concepts of dependence. Ann. Math. Statist. 37, 1137–1153 (1966)
Loynes, R.M.: An invariance principle for reverse martingales. Proc. Amer. Math. Soc. 25, 56–64 (1970)
Miller, R.G. Jr., Sen, P.K.: Weak convergence of U-statistics and von Mises' differentiable statistical functions. Ann. Math. Statist. 43, 31–41 (1972)
Neuhaus, G.: On weak convergence of stochastic processes with multi-dimensional time parameter. Ann. Math. Statist. 42, 1285–1295 (1971)
Puri, M.L., Sen, P.K.: Nonparametric Methods in Multivariate Analysis. New York: Wiley 1971
Sen, P.K.: Asymptotic sequential tests for regular functionals of distribution functions. Teoriya Veroyatnostei i ee Primeneniya 18, 235–249 (1973)
Sen, P.K.: An almost sure invariance principle for multivariate Kolmogorov-Smirnov statistics. Ann. Probab. 1, 488–496 (1973)
Sen, P.K.: Almost sure behavior of U-statistics and von Mises' differentiable statistical functions. Ann. Statist. 2, 387–395 (1974)
Sen, P.K., Ghosh, M.: On strong convergence of regression rank statistics. Sankhya, Ser. A, 34, 335–348 (1972)
Sen, P.K., Ghosh, M.: Sequential rank tests for location. Ann. Statist. 2, 540–552 (1974)
Strassen, V.: Almost sure behavior of sums of independent random variables and martingales. Proc. 5th Berkeley Symp. Math. Statist. Probab. 2, 315–343 (1967)
Wichura, M.J.: Some Strassen-type laws of the iterated logarithm for multiparameter stochastic processes with independent increments. Ann. Probab. 2, 272–296 (1973)
Author information
Authors and Affiliations
Additional information
Part of this work was done while the first author was visiting the Indian Statistical Institute, Calcutta.
Rights and permissions
About this article
Cite this article
Sen, P.K., Ghosh, M. Some invariance principles for rank statistics for testing independence. Z. Wahrscheinlichkeitstheorie verw Gebiete 29, 93–107 (1974). https://doi.org/10.1007/BF00532558
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00532558