We study the existence, strong consistency and asymptotic normality of estimators obtained from estimating functions, that are $p$-dimensional martingale transforms. The problem is motivated by the analysis of evolutionary clustered data, with distributions belonging to the exponential family, and which may also vary in terms of other component series. Within a quasi-likelihood approach, we construct estimating equations, which accommodate different forms of dependency among the components of the response vector and establish multivariate extensions of results on linear and generalized linear models, with stochastic covariates. Furthermore, we characterize estimating functions which are asymptotically optimal, in that they lead to confidence regions for the regression parameters which are of minimum size, asymptotically. Results from a simulation study and an application to a real dataset are included.

我们研究了从估计函数获得的估计的存在性，强一致性和渐近正态性，即 $p$mar变换。该问题是由于对演化聚类数据的分析而引起的，其分布属于指数族，并且在其他成分系列方面也可能有所不同。在一个拟似然方法中，我们构造了一个估计方程，这些方程容纳了响应矢量各组成部分之间的不同形式的依存关系，并在线性和广义线性模型上建立了具有随机协变量的结果的多元扩展。此外，我们表征了渐近最优的估计函数，因为它们导致了渐近最小参数的回归参数的置信区域。包括模拟研究的结果以及对实际数据集的应用。