  Large sample size brings the computation bottleneck for modern data analysis.
Subsampling is one of efficient strategies to handle this problem. In previous
studies, researchers make more fo- cus on subsampling with replacement (SSR)
than on subsampling without replacement (SSWR). In this paper we investigate a
kind of SSWR, poisson subsampling (PSS), for fast algorithm in ordinary
least-square problem. We establish non-asymptotic property, i.e, the error
bound of the correspond- ing subsample estimator, which provide a tradeoff
between computation cost and approximation efficiency. Besides the
non-asymptotic result, we provide asymptotic consistency and normality of the
subsample estimator. Methodologically, we propose a two-step subsampling
algorithm, which is efficient with respect to a statistical objective and
independent on the linear model assumption.. Synthetic and real data are used
to empirically study our proposed subsampling strategies. We argue by these
empirical studies that, (1) our proposed two-step algorithm has obvious
advantage when the assumed linear model does not accurate, and (2) the PSS
strategy performs obviously better than SSR when the subsampling ratio
increases.
