Best estimation of functional linear models

JOURNAL OF MULTIVARIATE ANALYSIS

卷:151

Article

Aletti, Giacomo^1,2  May, Caterina³  Tommasi, Chiara² 

[1] ADAMSS Ctr, Milan, Italy

[2] Univ Milan, Milan, Italy

[3] Univ Piemonte Orientale, Novara, Italy

关键词: Functional data analysis;    Sobolev spaces;    Linear models;    Repeated measurements;    Gauss-Markov theorem;    Riesz representation theorem;    Best linear unbiased estimator;   

DOI  :  10.1016/j.jmva.2016.07.005

来源: Elsevier

【 摘 要 】

Observations that are realizations of some continuous process are frequently found in science, engineering, economics, and other fields. In this paper, we consider linear models with possible random effects and where the responses are random functions in a suitable Sobolev space. In particular, the processes cannot be observed directly. By using smoothing procedures on the original data, both the response curves and their derivatives can be reconstructed, both as an ensemble and separately. From these reconstructed functions, one representative sample is obtained to estimate the vector of functional parameters. A simulation study shows the benefits of this approach over the common method of using information either on curves or derivatives. The main theoretical result is a strong functional version of the Gauss Markov theorem. This ensures that the proposed functional estimator is more efficient than the best linear unbiased estimator (BLUE) based only on curves or derivatives. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free