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随机解释变量下单调回归最小二乘估计的强一致性
In this paper it is shown that in the monotone regression model the unknown regression function can be consistently estimated by the least-squares method.
线性回归模型中最小二乘估计量的强相合性
For the linear regression model $y = X \beta + u$ with stochastic regressor matrix, strong consistency of the least squares estimator of $\beta$ is proved in the case of martingale difference errors and predetermined regressors and for the case where errors and regressors are orthogonal up to the second order. The results obtained are applied to parameter estimation in autoregressive processes, leading to strong consistency if the errors are quasi-independent up to the…
独立正态随机变量随机线性组合的收敛定理
It is shown that under fairly mild conditions linear combinations of independent normally distributed random variables with random coefficients tend to zero almost everywhere. The result is applied to parameter estimation in linear regression models.