  Subsampling is a computationally effective approach to extract information
from massive data sets when computing resources are limited. After a subsample
is taken from the full data, most available methods use an inverse probability
weighted (IPW) objective function to estimate the model parameters. The IPW
estimator does not fully utilize the information in the selected subsample. In
this paper, we propose to use the maximum sampled conditional likelihood
estimator (MSCLE) based on the sampled data. We established the asymptotic
normality of the MSCLE and prove that its asymptotic variance covariance matrix
is the smallest among a class of asymptotically unbiased estimators, including
the IPW estimator. We further discuss the asymptotic results with the L-optimal
subsampling probabilities and illustrate the estimation procedure with
generalized linear models. Numerical experiments are provided to evaluate the
practical performance of the proposed method.
