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Quasi-Likelihood for Median Regression Models

1996; Volume: 91; Issue: 433 Linguagem: Inglês

10.1080/01621459.1996.10476683

1537-274X

Sin‐Ho Jung,

Statistical Distribution Estimation and Applications

Abstract This article proposes quasi-likelihood equations for median regression models. The quasi-likelihood can be used for dependent observations such as repeated measurements or time series data. To construct a quasi-likelihood equation, we need to specify the relation between the median and the dispersion and also specify the dependency of the observations. If a monotone transformation of the original observation has a Laplace distribution, then the quasi-likelihood is the exact likelihood. Under moderate assumptions, the quasi-likelihood estimates are consistent and have asymptotically normal distributions. The estimates are also shown to have minimal asymptotic variance within a certain class of consistent estimates. The proposed method is illustrated using data from a clinical trial.