One of the most important assumptions in multiple regression analysis is the independence of the explanatory variables, however, this assumption is violated in several situations. In this work, we investigate regression equations when this independence does not hold and the explanatory variables are connected by many of elliptical copulas. We apply the proposed regression equation to study its heteroscedasticity diagnostic and using simulated data we also assess our regression model. A cross-validation procedure is carried out to ensure the unbiasedness of the results. Also, a real data analysis is presented as an application.
Assuming that CX,Y is the copula function of X and Y with marginal distribution functions FX (x) and FY (y), in this work we study the selection distribution Z d = (X|Y ∈ T ). We present some special cases of our proposed distribution, among them, skew-normal distribution as well as normal distribution. Some properties such as moments and moment generating function are investigated. Also, some numerical analysis is presented for illustration.
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