We show that the definition of the θth sample quantile as the solution to a minimization problem introduced by Koenker and Bassett (Econometrica 46(1):33-50, 1978) can be easily extended to obtain an analogous definition for the θth sample quantity quantile widely investigated and applied in the Italian literature. The key point is the use of the first-moment distribution of the variable instead of its distribution function. By means of this definition we introduce a linear regression model for quantity quantiles and analyze some properties of the residuals. In Sect. 4 we show a brief application of the methodology proposed.
Radaelli, P., Zenga, M. (2008). Quantity Quantiles Linear Regression. STATISTICAL METHODS & APPLICATIONS, 17(4), 455-469 [10.1007/s10260-007-0071-7].
Quantity Quantiles Linear Regression
RADAELLI, PAOLO
;ZENGA, MICHELE
2008
Abstract
We show that the definition of the θth sample quantile as the solution to a minimization problem introduced by Koenker and Bassett (Econometrica 46(1):33-50, 1978) can be easily extended to obtain an analogous definition for the θth sample quantity quantile widely investigated and applied in the Italian literature. The key point is the use of the first-moment distribution of the variable instead of its distribution function. By means of this definition we introduce a linear regression model for quantity quantiles and analyze some properties of the residuals. In Sect. 4 we show a brief application of the methodology proposed.
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