in the computer science literature; it can also be viewed as a naive parallel procedure. Please note that when we already have very large data sets in hand—as in many modern data analysis scenarios—we simply acquire new observations from an existing data set and ‘re-estimate’ the regression coefficients of the corresponding model; this situation is different from traditional sequential analysis applications, where we need to actually ‘collect’ new samples.

The remainder of this paper is organized as follows. In Section 2, we review the general sequential fixed-sized confidence region estimate, introduce our distributed sequential estimation procedure, discuss how to combine individual estimates into a final estimate when all procedures have finished, and study the method’s asymptotic properties. Furthermore, in Section 3, we present a sequential procedure with an ASE. Section 4 summarizes the numerical results by using the synthesized data and some real examples, including a data set pertaining to appliance energy use, and two fine particle/particulate matter (PM2.5) concentration data sets. Technical details are presented in the Appendix.

Distributed sequential estimation in linear models
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Consider a linear regression model, $$\begin{aligned}
\label{lm}
    Y={\bm{{X}}^{\top}} {\bm{{\beta}}} +\epsilon,\end{aligned}$$ where $Y \in R$ is a response variable, ${\bm{{X}}} \in {\bm{{R}}^{p}}$ is a covariate 