Topics in Continuous-Time Modeling

Abstract

We propose a unified approach to the estimation of the regression parameters under the double sampling design, in which a primary sample consisting of data on the rough or proxy measures for the response and/or explanatory variables, as well as a validation subsample consisting of data on the exact measurements, are available. Our proposal utilizes a specified parametric model to extract the partial information contained in the primary sample. The resulting estimator is consistent even if such model is misspecified, and achieves higher asymptotic efficiency than the estimator based only on the validation data. Specific cases are discussed to illustrate the application of the proposed estimator.