Advances and Applications in Statistics
Volume 44, Issue 2, Pages 133 - 143
(February 2015) http://dx.doi.org/10.17654/ADASFeb2015_133_143 |
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A PARAMETRIC APPROACH FOR ESTIMATING CONDITIONAL PROBABILITY DISTRIBUTIONS
T. K. Mak and F. Nebebe
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Abstract: We consider in this paper a fully parametric approach that directly models the conditional distribution of a response variable as a function of the explanatory variables using a class of probability distributions recently proposed in Mak and Nebebe [4]. A fully parametric approach, unlike traditional quantile regression which fits a quantile regression function for each quantile, yields automatically an estimate of the quantile regression function for any quantile once the parameters in the model have been estimated. Furthermore, statistical inferences on how the conditional distribution varies with the values of the explanatory variables are considerably easier with the proposed parametric modeling than quantile regression. We also studied the relationship between quantile regression and the present approach under linear modeling. A real example using a real estate data set is used to illustrate the proposed methodology. |
Keywords and phrases: conditional distributions, non-normal probability distributions, quantile regression. |
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