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Penalized wavelet monotone regression
- Source :
- Statistics and Probability Letters, Statistics and Probability Letters, 2007, 77 (16), pp.1608-1621. ⟨10.1016/j.spl.2007.03.041⟩, Statistics and Probability Letters, Elsevier, 2007, 77 (16), pp.1608-1621. ⟨10.1016/j.spl.2007.03.041⟩
- Publication Year :
- 2007
- Publisher :
- Elsevier BV, 2007.
-
Abstract
- International audience; In this paper we focus on nonparametric estimation of a constrained regression function using penalized wavelet regression techniques. This results into a convex optimization problem under linear constraints. Necessary and sufficient conditions for existence of a unique solution are discussed. The estimator is easily obtained via the dual formulation of the optimization problem. In particular we investigate a penalized wavelet monotone regression estimator. We establish the rate of convergence of this estimator, and illustrate its finite sample performance via a simulation study. We also compare its performance with that of a recently proposed constrained estimator. An illustration to some real data is given.
- Subjects :
- Splines
Statistics and Probability
Monotonicity
Statistics::Theory
Mathematical optimization
Optimization problem
Wavelets
01 natural sciences
Statistics::Machine Learning
010104 statistics & probability
Minimum-variance unbiased estimator
Wavelet
Constrained curve fitting
[MATH.MATH-ST]Mathematics [math]/Statistics [math.ST]
0502 economics and business
Statistics::Methodology
0101 mathematics
Wavelet nonparametric regression
050205 econometrics
Mathematics
Wavelet thresholding
05 social sciences
Constrained optimization
Estimator
[STAT.TH]Statistics [stat]/Statistics Theory [stat.TH]
MSC: 62G07, 65Dxx
Nonparametric regression
Besov spaces
Convex optimization
Statistiques
Statistics, Probability and Uncertainty
Minimax estimator
Subjects
Details
- ISSN :
- 01677152
- Volume :
- 77
- Database :
- OpenAIRE
- Journal :
- Statistics & Probability Letters
- Accession number :
- edsair.doi.dedup.....8a73a5eb56833bf5dcf9bb3524b3063a