In this paper, we propose a broad and general sequential sampling scheme,
which incorporates four different types of sampling procedures: i) the classic
Anscombe-Chow-Robbins purely sequential sampling procedure; ii) the ordinary
accelerated sequential sampling procedure; iii) the relatively new k-at-a-time
purely sequential sampling procedure; iv) the new k-at-a-time improved
accelerated sequential sampling procedure. The first-order and second-order
properties of this general sequential sampling scheme are fully investigated
with two illustrations on minimum risk point estimation for the mean of a
normal distribution and on bounded variance point estimation for the location
parameter of a negative exponential distribution, respectively. We also provide
extensive computational simulation studies and real data analyses for each
illustration