
Density deconvolution under general assumptions on the distribution of measurement errors
In this paper we study the problem of density deconvolution under genera...
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Nonparametric Bayesian Deconvolution of a Symmetric Unimodal Density
We consider nonparametric measurement error density deconvolution subjec...
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Density Deconvolution with NonStandard Error Distributions: Rates of Convergence and Adaptive Estimation
It is a typical standard assumption in the density deconvolution problem...
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Statistical deconvolution of the free FokkerPlanck equation at fixed time
We are interested in reconstructing the initial condition of a nonlinea...
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A frequency domain analysis of the error distribution from noisy highfrequency data
Data observed at high sampling frequency are typically assumed to be an ...
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The index of increase in the presence of measurement errors and the inevitability of striking a balance between determinism and randomness
We introduce a modification of the index of increase that works in both ...
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Nonclassical Measurement Error in the Outcome Variable
We study a semi/nonparametric regression model with a general form of n...
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A splineassisted semiparametric approach to nonparametric measurement error models
Nonparametric estimation of the probability density function of a random variable measured with error is considered to be a difficult problem, in the sense that depending on the measurement error prop erty, the estimation rate can be as slow as the logarithm of the sample size. Likewise, nonparametric estimation of the regression function with errors in the covariate suffers the same possibly slow rate. The traditional methods for both problems are based on deconvolution, where the slow convergence rate is caused by the quick convergence to zero of the Fourier transform of the measurement error density, which, unfortunately, appears in the denominators during the con struction of these methods. Using a completely different approach of splineassisted semiparametric methods, we are able to construct nonparametric estimators of both density functions and regression mean functions that achieve the same nonparametric convergence rate as in the error free case. Other than requiring the errorprone variable distribution to be compactly supported, our assumptions are not stronger than in the classical deconvolution literatures. The performance of these methods are demonstrated through some sim ulations and a data example.
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