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New M-estimators in semi-parametric regression with errors in variables

Cristina Butucea, Marie-Luce Taupin (2008)

Annales de l'I.H.P. Probabilités et statistiques

In the regression model with errors in variables, we observe n i.i.d. copies of (Y, Z) satisfying Y=fθ0(X)+ξ and Z=X+ɛ involving independent and unobserved random variables X, ξ, ɛ plus a regression function fθ0, known up to a finite dimensional θ0. The common densities of the Xi’s and of the ξi’s are unknown, whereas the distribution of ɛ is completely known. We aim at estimating the parameter θ0 by using the observations (Y1, Z1), …, (Yn, Zn). We propose an estimation procedure based on the least...

Nonparametric regression estimation based on spatially inhomogeneous data: minimax global convergence rates and adaptivity

Anestis Antoniadis, Marianna Pensky, Theofanis Sapatinas (2014)

ESAIM: Probability and Statistics

We consider the nonparametric regression estimation problem of recovering an unknown response function f on the basis of spatially inhomogeneous data when the design points follow a known density g with a finite number of well-separated zeros. In particular, we consider two different cases: when g has zeros of a polynomial order and when g has zeros of an exponential order. These two cases correspond to moderate and severe data losses, respectively. We obtain asymptotic (as the sample size increases)...

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