论文标题
马尔可夫线性模型中平均值和方差的估计
Estimations of means and variances in a Markov linear model
论文作者
论文摘要
多元回归模型和方差分析可能是所有统计分析中最常用的方法。我们研究了预测因子是定性变量的情况，并且响应变量是定量的。在这种情况下，我们提出了不假定同质性的经典方法的替代方法，但假设马尔可夫链可以描述协变量的相关性。这种方法使用对独立协变量的度量更改转换了依赖的协变量。转化的估计值允许对协变量不同值的贡献的均值和方差进行成对比较。我们表明，在标准力矩条件下，估计器在渐变上是正态分布的。我们使用模拟数据测试我们的方法，并将其应用于几个经典数据集。
Multivariate regression models and ANOVA are probably the most frequently applied methods of all statistical analyses. We study the case where the predictors are qualitative variables, and the response variable is quantitative. In this case, we propose an alternative to the classic approaches that does not assume homoscedasticity but assumes that a Markov chain can describe the covariates' correlations. This approach transforms the dependent covariates using a change of measure to independent covariates. The transformed estimates allow a pairwise comparison of the mean and variance of the contribution of different values of the covariates. We show that under standard moment conditions, the estimators are asymptotically normally distributed. We test our method with data from simulations and apply it to several classic data sets.
