A review on recent advances and applications of h-likelihood method

Having spent almost 30 years since Lee and Nelder introduced the h-likelihood at the discussion meeting held in Royal Statistical Society in 1994, Lee and his colleagues and students have studied how to define the h-likelihood for complex statistical models and conduct inference about unobservables and fixed unknown parameters in them. In this paper we review several important research areas with a focus on how the h-likelihood method has been applied. This review covers areas including analysis of clustered survival data, competing risk models with frailty, joint models for longitudinal and survival outcomes, sparse high-dimensional multivariate analysis, spatial analysis and multiple testing.