在统计学中，高斯－马尔可夫定理陈述的是：在误差零均值，同方差，且互不相关的线性回归模型中，回归系数的最佳线性无偏估计（BLUE）就是最小方差估计。一般而言，任何回归系数的线性组合之BLUE就是它的最小方差估计。在这个线性回归模型中，其误差不需要假定为正态分布或独立同分布（iid）（而仅需要满足不相关和同方差这两个稍弱的条件）。

具体而言，假设

其中β₀和β₁是非随机且未观测到的参数，x_i 是观测到的变量，ε_i是随机误差，Y_i是随机变量（x小写:因x非为随机变量，Y大写:因Y为随机变量）。

高斯－马尔可夫定理的条件是：

In statistics, the Gauss–Markov theorem, named after Carl Friedrich Gauss and Andrey Markov, states that in a linear regression model in which the errors have expectation zero and are uncorrelated and have equal variances, the best linear unbiased estimator (BLUE) of the coefficients is given by the ordinary least squares (OLS) estimator. Here "best" means giving the lowest variance of the estimate, as compared to other unbiased, linear estimators. The errors do not need to be normal, nor do they need to be independent and identically distributed (only uncorrelated with mean zero and homoscedastic with finite variance). The requirement that the estimator be unbiased cannot be dropped, since biased estimators exist with lower variance. See, for example, the James–Stein estimator (which also drops linearity) or ridge regression.