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

JOURNAL OF MULTIVARIATE ANALYSIS

卷:146

Article

Demongeot, Jacques¹  Hamie, Ali¹  Laksaci, Ali²  Rachdi, Mustapha³ 

[1] Univ Grenoble 1, Fac Med Grenoble, Univ Grenoble Alpes, Lab AGIM,FRE 3405,CNRS, F-38700 La Tronche, France

[2] Univ Djillali Liabes Sidi Bel Abbes, Lab Stat & Proc Stochast, BP 89, Sidi Bel Abbes 22000, Algeria

[3] Univ Grenoble Alpes, Lab AGIM, FRE 3405, CNRS,UPMF,UFR SHS, BP 47, F-38040 Grenoble 09, France

关键词: Mean square relative error;    Nonparametric estimation;    Functional data;    Regression operator;    Positive responses;    Asymptotic normality;    Small ball property;    Stock price;    Economic data;   

DOI  :  10.1016/j.jmva.2015.09.019

来源: Elsevier

【 摘 要 】

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. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

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