In this work a general semi-parametric multivariate model where the first two conditional moments are assumed to be multivariate time series is introduced. The focus of the estimation is the conditional mean parameter vector for discrete-valued distributions. Quasi-Maximum Likelihood Estimators (QMLEs) based on the linear exponential family are typically employed for such estimation problems when the true multivariate conditional probability distribution is unknown or too complex. Although QMLEs provide consistent estimates they may be inefficient. In this paper novel two-stage Multivariate Weighted Least Square Estimators (MWLSEs) are introduced which enjoy the same consistency property as the QMLEs but can provide improved efficiency with suitable choice of the covariance matrix of the observations. The proposed method allows for a more accurate estimation of model parameters in particular for count and categorical data when maximum likelihood estimation is unfeasible. Moreover, consistency and asymptotic normality of MWLSEs are derived. The estimation performance of QMLEs and MWLSEs is compared through simulation experiments and a real data application, showing superior accuracy of the proposed methodology.

翻译：本文提出了一种通用的半参数多元模型，其中前两个条件矩被假定为多元时间序列。估计的重点是离散值分布的条件均值参数向量。当真实的多元条件概率分布未知或过于复杂时，通常采用基于线性指数族的拟极大似然估计量(QMLEs)来处理此类估计问题。尽管QMLEs能提供一致估计，但可能效率较低。本文引入了新颖的两阶段多元加权最小二乘估计量(MWLSEs)，其具有与QMLEs相同的一致性性质，但通过适当选择观测值的协方差矩阵，可提高估计效率。当极大似然估计不可行时，所提方法能更精确地估计模型参数，尤其适用于计数数据和分类数据。此外，还推导了MWLSEs的一致性和渐近正态性。通过仿真实验和实际数据应用，比较了QMLEs和MWLSEs的估计性能，结果表明所提方法具有更高的精度。