6533b835fe1ef96bd129f749
RESEARCH PRODUCT
Thresholding projection estimators in functional linear models
Jan JohannesHervé Cardotsubject
FOS: Computer and information sciencesStatistics and ProbabilityMathematical optimizationStatistics::TheoryMean squared error of predictionMean squared errorMathematics - Statistics TheoryStatistics Theory (math.ST)Projection (linear algebra)Methodology (stat.ME)FOS: MathematicsApplied mathematicsStatistics - MethodologyMathematicsLinear inverse problemNumerical AnalysisLinear modelEstimatorRegression analysisMinimaxSobolev spaceThresholdingOptimal rate of convergenceDerivatives estimationRate of convergenceHilbert scaleStatistics Probability and UncertaintyGalerkin methoddescription
We consider the problem of estimating the regression function in functional linear regression models by proposing a new type of projection estimators which combine dimension reduction and thresholding. The introduction of a threshold rule allows to get consistency under broad assumptions as well as minimax rates of convergence under additional regularity hypotheses. We also consider the particular case of Sobolev spaces generated by the trigonometric basis which permits to get easily mean squared error of prediction as well as estimators of the derivatives of the regression function. We prove these estimators are minimax and rates of convergence are given for some particular cases.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2008-06-03 | Journal of Multivariate Analysis |