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Linear functional regression: The case of fixed design and functional response
Author(s) -
Cuevas Antonio,
Febrero Manuel,
Fraiman Ricardo
Publication year - 2002
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315952
Subject(s) - estimator , consistency (knowledge bases) , linear regression , mathematics , simple linear regression , simple (philosophy) , regression , proper linear model , fixed point , regression analysis , bayesian multivariate linear regression , design matrix , mathematical optimization , computer science , statistics , discrete mathematics , mathematical analysis , philosophy , epistemology
The authors consider the problem of simple linear regression when the exogenous and endogenous variables are functional and the design is fixed. They propose an estimator for the underlying linear operator and prove its consistency under some conditions which ensure that the design is sufficiently informative. They consider the classical calibration (or inverse regression) problem and analyze a consistent estimator. They also give a simulation study. The proposed method is not hard to implement in practice.