Statistical Issues on Instrumental Scores for Non-likelihood Stochastic Models

Abstract

For the data exhibiting a dependency structure, the exact likelihood is rarely available to researchers mainly because of unobserved initial values and unknown innovation distributions. It is the case in practice to assume a tractable score for the data for the sake of easy analysis. The adopted tractable score is referred to as the instrumental score in order to discriminate from the true Fisher’s score. In this review paper, various existing inferential methodologies in stochastic models (e.g., conditional least squares, pseudo likelihood, quasi-likelihood, quasi-maximum likelihood, Godambe’s linear scores) are reviewed under a unified framework of the instrumental scores. Applications to bifurcating auto-regressions in the context of cell lineage studies are discussed.