Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-23T18:16:00.144Z Has data issue: false hasContentIssue false
  • English
  • Français

Some applications of weak convergence to statistics

Published online by Cambridge University Press:  14 July 2016

R. M. Loynes
Get access Rights & Permissions [Opens in a new window]

Abstract

Results showing the weak convergence of certain stochastic processes are used to derive both known and new (asymptotic) properties of signs of residuals from regression; other weak convergence results are derived, and used to determine the behaviour of runs of residuals.

Keywords

REGRESSION RESIDUALSRUNSWEIGHTED EMPIRICAL DISTRIBUTION FUNCTION
Type
Part 5 - Concepts of Coincidence and Convergence
Information
Journal of Applied Probability , Volume 25 , Issue A , 1988 , pp. 201 - 211
Copyright
Copyright © Applied Probability Trust 1988 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Billingsley, P. (1968) Convergence of Probability Measures. Wiley, New York.Google Scholar
Brown, B. M. (1975) A short-cut test for outliers using residuals. Biometrika 62, 623–629.Google Scholar
Brown, B. M. and Kildea, D. G. (1979) Outlier detection tests and robust estimators based on signs of residuals. Comm. Statist. Theory Meth. A8, 257–269.Google Scholar
Cox, D. R. and Snell, E. J. (1968) A general definition of residuals. J. R. Statist. Soc. B 30, 248–275.Google Scholar
David, H. T. (1962) The sample mean among the moderate order statistics. Ann. Math. Statist. 33, 1160–1166.Google Scholar
Koul, H. L. (1984) Tests of goodness-of-fit in linear regression. Coll. Math. Soc. Janos Bólyai 45, 279–315.Google Scholar
Loynes, R. M. (1980) The empirical distribution function of residuals from generalised regression. Ann. Statist. 8, 285–298.CrossRefGoogle Scholar
Mukantseva, L. A. (1977) Testing normality in one-dimensional and multidimensional linear regression. Theory Prob. Appl. 22, 591–602.Google Scholar
Pierce, D. A. and Kopecky, K. J. (1979) Testing goodness-of-fit for the distribution of errors in regression. Biometrika 66, 1–5.Google Scholar
Withers, C. S. (1975) Convergence of empirical processes of mixing rv's on [0, 1]. Ann. Statist. 3, 1101–1108.Google Scholar
Wood, C. L. (1978) A large-sample Kolmogorov-Smirnov test for normality of experimental error in a randomized block design. Biometrika 65, 673–676.Google Scholar