Biostatistics Commons^™

A Spline-Assisted Semiparametric Approach To Nonparametric Measurement Error Models, Fei Jiang, Yanyuan Ma

COBRA Preprint Series

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 …