A combined method based on kurtosis indexes for estimating p in non linear Lp-norm regression

The Generalized Error Distribution (G.E.D.) is a very flexible family of symmetric density distributions, which are characterized by their shape parameter p linked to the L p -norm estimators. In fact, under this errors assumption in the regression model the G.E.D. parameter p coincides with the p exponent of the L p -norm . In this paper, we examine the use of Lp -norm estimators in the framework of non-linear regression models assuming the G.E.D. as the errors distribution. More precisely, we introduce an exponential regression (Markovi ć, & Borozan, 2015) and a new algorithm Lp med consisting of two iterative procedures, one internal to estimate the regression parameters and another external for estimating p (the p exponent of the L p -norm ) based on two kurtosis indexes of the residuals distribution. In order to show the good results of the proposed method, an efficiency comparison of the new method, Lp med , with other two well-known approaches as the maximum likelihood (Agrò, 1995) and the Money et al. (1982) method is performed. Our combined method shows better results asymptotically and, especially in presence of leptokurtic data, for the p parameter estimation. Finally an application on the Equitable and Sustainable Well-being (B.E.S) in the Italian context confirms the good properties of the proposed method