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In the multidimensional setting, we consider the nonparametric regression estimation with errors-in-variables. Both ordinary smooth noise and super smooth one are assumed for errors in the covariates. An anisotropic kernel estimator is provided based on a deconvolution technique. We study the pointwise estimation and obtain the optimal rates of convergence under the anisotropic Hölder condition. [ABSTRACT FROM AUTHOR]

Using a wavelet basis, this article considers the mean integrated squared error (MISE) of linear and non linear wavelet estimators for regression derivatives r (d) (x) based on biased strong mixing data. It turns out that the convergence rates coincide with those of Chesneau and Shirazi's (Communication in Statistics-Theory and Methods, 2014), when d = 0 and the random sample is independent. [ABSTRACT FROM AUTHOR]

This paper considers wavelet estimations for a regression function based on negatively associated data. We provide upper bounds of mean integrated squared error of wavelet estimators in Besov space. It turns out that our theorem reduces to the theorem of Chesneau and Shirazi [Nonparametric wavelet regression based on biased data. Comm Statist Theory Methods. 2014;43:2642–2658], when the random sample is independent. [ABSTRACT FROM AUTHOR]

This paper considers non linear wavelet estimation on risk for the derivatives of regression function in Besov spaces based on biased data. It turns out that the convergence rate of non linear wavelet estimator keeps the same as Chaubey, Chesneau and Navarro's linear estimator (Linear wavelet estimation of the derivatives of a regression function based on biased data, Communication in Statistics-Theory and Methods, 46: 9541-9556, 2017), when. However, the non linear estimator gets better if. On the other hand, our estimator is adaptive. Finally, our theory is illustrated with a simulation study. [ABSTRACT FROM AUTHOR]

In practical applications, people sometimes do not know whether the estimated function is smooth, and it is reasonable to consider the consistency of an estimator. Furthermore, the acquired data are usually contaminated by various random noises. In this paper, we develop the wavelet estimators for m -fold convolutions of the unknown density functions and consider their L p ( 1 ≤ p < ∞ ) consistency under noiseless and additive noise situations, respectively. Finally, simulation studies illustrate the good performances of our nonparametric wavelet estimators. [ABSTRACT FROM AUTHOR]

This paper studies the regression estimation with errors-in-variables. We first extend Meister's theorems (Meister, 2009. Deconvolution Problems in Nonparametric Statistics. Springer, Berlin) from one to multi-dimensional setting, when a noise density has no zeros in the Fourier domain. Then motivated by the work of Delaigle and Meister (Delaigle, Meister, 2011. Nonparametric function estimation under Fourier-oscillating noise. Statistica Sinica 21, 1065-1092), we show a desired convergence rate of a kernel estimator for Fourier-oscillating noises. Finally, two technical conditions are removed, when a wavelet estimator is used. [ABSTRACT FROM AUTHOR]