  Blocking, a special case of rerandomization, is routinely implemented in the
design stage of randomized experiments to balance the baseline covariates. This
study proposes a regression adjustment method based on the least absolute
shrinkage and selection operator (Lasso) to efficiently estimate the average
treatment effect in randomized block experiments with high-dimensional
covariates. We derive the asymptotic properties of the proposed estimator and
outline the conditions under which this estimator is more efficient than the
unadjusted one. We provide a conservative variance estimator to facilitate
valid inferences. Our framework allows one treated or control unit in some
blocks and heterogeneous propensity scores across blocks, thus including paired
experiments and finely stratified experiments as special cases. We further
accommodate rerandomized experiments and a combination of blocking and
rerandomization. Moreover, our analysis allows both the number of blocks and
block sizes to tend to infinity, as well as heterogeneous treatment effects
across blocks without assuming a true outcome data-generating model. Simulation
studies and two real-data analyses demonstrate the advantages of the proposed
method.
