We consider integrating a non‐probability sample with a probability sample which provides high dimensional representative covariate information of the target population. We propose a two‐step approach for variable selection and finite population inference. In the first step, we use penalized estimating equations with folded concave penalties to select important variables and show selection consistency for general samples. In the second step, we focus on a doubly robust estimator of the finite population mean and re‐estimate the nuisance model parameters by minimizing the asymptotic squared bias of the doubly robust estimator. This estimating strategy mitigates the possible first‐step selection error and renders the doubly robust estimator root n consistent if either the sampling probability or the outcome model is correctly specified.

中文翻译：

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将概率样本和非概率样本与高维数据组合时的双稳健推断

我们考虑将非概率样本与概率样本相集成，该样本提供目标人群的高维代表性协变量信息。我们为变量选择和有限总体推断提出了一种两步法。第一步，我们使用带有折叠凹痕罚分的罚估计方程来选择重要变量并显示一般样本的选择一致性。在第二步中，我们专注于有限总体均值的双稳健估计器，并通过最小化双稳健估计器的渐近平方偏差来重新估计扰动模型参数。这种估计策略减轻了可能的第一步选择错误，并使双重鲁棒的估计器根n 如果正确指定了采样概率或结果模型，则保持一致。