Zeger S L, Qaqish B
Department of Biostatistics, Johns Hopkins University, Baltimore, Maryland 21205.
Biometrics. 1988 Dec;44(4):1019-31.
This paper discusses a quasi-likelihood (QL) approach to regression analysis with time series data. We consider a class of Markov models, referred to by Cox (1981, Scandinavian Journal of Statistics 8, 93-115) as "observation-driven" models in which the conditional means and variances given the past are explicit functions of past outcomes. The class includes autoregressive and Markov chain models for continuous and categorical observations as well as models for counts (e.g., Poisson) and continuous outcomes with constant coefficient of variation (e.g., gamma). We focus on Poisson and gamma data for illustration. Analogous to QL for independent observations, large-sample properties of the regression coefficients depend only on correct specification of the first conditional moment.
本文讨论了一种用于时间序列数据回归分析的拟似然（QL）方法。我们考虑一类马尔可夫模型，考克斯（1981年，《斯堪的纳维亚统计杂志》8，93 - 115）将其称为“观测驱动”模型，其中给定过去情况下的条件均值和方差是过去结果的显式函数。该类别包括用于连续和分类观测的自回归和马尔可夫链模型，以及用于计数（如泊松分布）和具有恒定变异系数的连续结果（如伽马分布）的模型。为便于说明，我们重点关注泊松分布和伽马分布数据。类似于独立观测的拟似然方法，回归系数的大样本性质仅取决于第一个条件矩的正确设定。
