Abstract
Nonparametric statistics is concerned with the development of distribution free methods to solve various statistical problems. Examples include tests for a monotonic trend, or tests of hypotheses that two samples come from the same distribution. One of the important tools in nonparametric statistics is the use of ranking data. When the data is transformed into ranks, one gains the simplicity that objects may be more easily compared. For example, if web pages are ranked in accordance to some criterion, one obtains a quick summary of choices. In this chapter, we will study linear rank statistics which are functions of the ranks.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Bhattacharya, R., Lizhen, L., and Patrangenaru, V. (2016). A Course in Mathematical Statistics and Large Sample Theory. Springer.
Diaconis, P. and Graham, R. (1977). Spearman’s footrule as a measure of disarray. Journal of the Royal Statistical Society Series B, 39:262–268.
Ferguson, T. (1996). A Course in Large Sample Theory. John Wiley and Sons.
Gibbons, J. D. and Chakraborti, S. (2011). Nonparametric Statistical Inference. Chapman Hall, New York, 5th edition.
Gotze, F. (1987). Approximations for multivariate U statistics. Journal of Multivariate Analysis, 22:212–229.
Hajek, J. (1968). Asymptotic normality of simple linear rank statistics under alternatives. Ann. Math. Statist., 39:325–346.
Hájek, J. and Sidak, Z. (1967). Theory of Rank Tests. Academic Press, New York.
Hoeffding, W. (1948). A class of statistics with asymptotically normal distribution. Annals of Mathematical Statistics, 19:293–325.
Hoeffding, W. (1951a). A combinatorial central limit theorem. Annals of Mathematical Statistics, 22:558–566.
Lee, A. (1990). U-Statistics. Marcel Dekker Inc., New York.
Lehmann, E. (1975). Nonparametrics: Statistical Methods Based on Ranks. McGraw-Hill, New York.
Randles, Ronald, H. and Wolfe, Douglas, A. (1979). Introduction to the Theory of Nonparametric Statistics. John Wiley and Sons, Inc.
van der Vaart, A. (2007). Asymptotic Statistics. Cambridge University Press.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Alvo, M., Yu, P.L.H. (2018). Tools for Nonparametric Statistics. In: A Parametric Approach to Nonparametric Statistics. Springer Series in the Data Sciences. Springer, Cham. https://doi.org/10.1007/978-3-319-94153-0_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-94153-0_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-94152-3
Online ISBN: 978-3-319-94153-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)