Cramér-von Mises regression

Kilani Ghoudi, David McDonald

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


Consider a linear regression model with unknown regression parameters β0 and independent errors of unknown distribution. Block the observations into q groups whose independent variables have a common value and measure the homogeneity of the blocks of residuals by a Cramér-von Mises q-sample statistic Tq(β). This statistic is designed so that its expected value as a function of the chosen regression parameter β has a minimum value of zero precisely at the true value β0. The minimizer β̂ of Tq(β) over all β is shown to be a consistent estimate of β0. It is also shown that the bootstrap distribution of Tq0) can be used to do a lack of fit test of the regression model and to construct a confidence region for β0.

Original languageEnglish
Pages (from-to)689-714
Number of pages26
JournalCanadian Journal of Statistics
Issue number4
Publication statusPublished - Dec 2000
Externally publishedYes


  • Bootstrap distribution
  • Confidence region
  • Estimation
  • Nonparametric regression
  • Randomness statistics

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


Dive into the research topics of 'Cramér-von Mises regression'. Together they form a unique fingerprint.

Cite this