Extrapolation in parametric models with Laplace measurement error

Abstract

For general parametric statistical models with some variables being contaminated with the Laplace measurement error, we propose an extrapolation algorithm to estimate the unknown parameters. By applying the conditional expectation directly to the target function, either the function to be optimized or an estimation equation, the proposed algorithm successfully bypasses the simulation step in the classical simulation extrapolation procedure and thus provides a viable alternative to the classical simulation extrapolation algorithm. Large sample properties of the resulting estimator are discussed. Finite sample performance of the proposed extrapolation estimation procedure is demonstrated by examples and numerical simulation studies.