Density estimation from noisy observations of a stochastic process

Martin Sköld

Abstract:: We consider a new approach to non-parametric density estimation for stochastic processes observed with noise. By assuming the data are sampled from a smooth continuous-time process plus independent noise we reconstruct the original process by regression analysis and estimate the density by continuous-time kernel methods. We find asymptotic bias and variance of the estimator and apply to finding rate-optimal sampling schemes.
Key words:: Non-parametric density estimation, kernel smoothing, errors-in-variables, deconvolution, dependent data, interpolation.