Regression analysis and dependence

José M. González-Barrios and Silvia Ruiz-Velasco

Metrika: International Journal for Theoretical and Applied Statistics, 2005, vol. 61, issue 1, 73-87

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

Keywords: Regresion analysis; Nonlinear models; Multivariate dependency measures; Copulas; Model selection (search for similar items in EconPapers)
Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:spr:metrik:v:61:y:2005:i:1:p:73-87

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DOI: 10.1007/s001840400325

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