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Regression analysis and dependence

Author

Listed:
  • José M. González-Barrios
  • Silvia Ruiz-Velasco

Abstract

In this paper we study the relationship between regression analysis and a multivariate dependency measure. If the general regression model Y=f([InlineMediaObject not available: see fulltext.]) holds for some function f, where 1≤i 1 > i 2 >···i m ≤k, and X 1 ,...,X k is a set of possible explanatory random variables for Y. Then there exists a dependency relation between the random variable Y and the random vector ([InlineMediaObject not available: see fulltext.]). Using the dependency statistic [InlineMediaObject not available: see fulltext.] defined below, we can detect such dependency even if the function f is not linear. We present several examples with real and simulated data to illustrate this assertion. We also present a way to select the appropriate subset [InlineMediaObject not available: see fulltext.] among the random variables X 1 ,X 2 ,...,X k , which better explain Y. Copyright Springer-Verlag 2005

Suggested Citation

  • José M. González-Barrios & Silvia Ruiz-Velasco, 2005. "Regression analysis and dependence," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 61(1), pages 73-87, February.
    • Handle: RePEc:spr:metrik:v:61:y:2005:i:1:p:73-87
    DOI: 10.1007/s001840400325
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