Parameters of a linear regression model can be estimated with the help of traditional methods like generalized least squares and mixed estimator. However, recent developments increased the importance of big data sets, which have much more predictors than observations where some predictors have no impact on the dependent variable. The estimation and model selection problem of big datasets can be solved using the least absolute shrinkage and selection operator (Lasso). However, to the authors’ knowledge, there is no study that incorporates stochastic restrictions, within a Lasso framework. In this paper, we propose a Mixed Lasso (M-Lasso) estimator that incorporates stochastic linear restrictions to big data sets for selecting the true model and estimating parameters simultaneously. We conduct a simulation study to compare the performance of M-Lasso with existing estimators based on mean squared error $(\text{mse})$ and model selection performance. Results show that M-Lasso is superior in terms of $\text{mse}$ and it generally dominates compared estimators according to the model selection criteria. We employ M-Lasso to estimate parameters of a widely analysed production function under stochastic restrictions raised from economic theory. Our results show that M-Lasso can provide reasonable and more precise estimates of model parameters that are in line with the economic theory.

线性回归模型的参数可以借助广义最小二乘法和混合估计器等传统方法进行估计。然而，最近的发展增加了大数据集的重要性，大数据集的预测变量比某些预测变量对因变量没有影响的观察结果要多得多。大数据集的估计和模型选择问题可以使用最小绝对收缩和选择算子（Lasso）来解决。然而，据作者所知，还没有研究在 Lasso 框架内纳入随机限制。在本文中，我们提出了一种混合套索（M-Lasso）估计器，它将随机线性限制纳入大数据集，以同时选择真实模型和估计参数。我们进行了一项模拟研究，将 M-Lasso 的性能与基于均方误差的现有估计器进行比较 和模型选择性能。结果表明，M-Lasso 在以下方面更胜一筹 $\text{<span data-immersive-translate-walked="75facb84-ff87-49c0-9beb-7e210b47d86b">硕士</span>}$根据模型选择标准，它通常在比较估计器中占主导地位。我们使用 M-Lasso 来估计在经济理论提出的随机限制下广泛分析的生产函数的参数。我们的结果表明，M-Lasso 可以提供符合经济理论的合理且更精确的模型参数估计。