Relative-error prediction in nonparametric functional statistics: Theory and practice

Abstract

In this paper, an alternative kernel estimator of the regression operator of a scalar response variable Y given a random variable X taking values in a semi-metric space is considered. The constructed estimator is based on the minimization of the mean squared relative error. This technique is useful in analyzing data with positive responses, such as stock prices or life times. Least squares or least absolute deviation are among the most widely used criteria in statistical estimation for regression models. However, in many practical applications, especially in treating, for example, the stock price data, the size of the relative error rather than that of the error itself, is the central concern of the practitioners. This paper offers then an alternative to traditional estimation methods by considering the minimization of the least absolute relative error for operatorial regression models. We prove the strong and the uniform consistencies (with rates) of the constructed estimator. Moreover, the mean squared convergence rate is given and the asymptotic normality of the proposed estimator is proved. Finally, supportive evidence is shown by simulation studies and an application on some economic data was performed.