<p>Morden data with considerable size and large dimension are widely encountered in practice. Moreover, the responses of massive data are sometimes hard to obtain due to high cost and privacy protection. For generalized linear models (GLMs) in increasing dimension, this paper investigates optimal response-free Poisson subsampling. We first propose an inverse probability weighted subsample estimator and theoretical results under unconditional framework are established. The optimal response-free probabilities are derived through L-optimality criterion for increasing dimension, and a two-step algorithm is considered to meet practical needs. To further enhance the estimation efficiency, a more efficient unweighted estimator is constructed based on the optimal subsample. The satisfactory performance of our proposed subsample estimators are illustrated by both simulation studies and two real world applications.</p>

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Optimal response-free Poisson subsampling for generalized linear models in increasing dimension

  • Junhao Shan,
  • Lei Wang

摘要

Morden data with considerable size and large dimension are widely encountered in practice. Moreover, the responses of massive data are sometimes hard to obtain due to high cost and privacy protection. For generalized linear models (GLMs) in increasing dimension, this paper investigates optimal response-free Poisson subsampling. We first propose an inverse probability weighted subsample estimator and theoretical results under unconditional framework are established. The optimal response-free probabilities are derived through L-optimality criterion for increasing dimension, and a two-step algorithm is considered to meet practical needs. To further enhance the estimation efficiency, a more efficient unweighted estimator is constructed based on the optimal subsample. The satisfactory performance of our proposed subsample estimators are illustrated by both simulation studies and two real world applications.