$N_j$ for each $j$, and because we run several procedures concurrently, the computation time will be smaller (as expected). However, it is worthwhile to note that when the number of variables increases or the procedure involves variable selection, the differences in computation times will increase. In addition, because the proposed procedure combines the estimation results of each procedure (each of which features a different data size), it is more stable than that of a single procedure in terms of coverage probabilities and the like. In our numerical studies, we will compare performance levels by using different $M$ values.

Active learning with D-optimal design criterion
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In the machine learning literature, the term ‘active learning’ usually refers to some learning algorithms that can interactively query users. From statistical modelling perspectives, this concept approximates subject selection. The work of [@Deng2009]—which extends that of [@JeffWu1985] and closely relates to that of [@robbins1951; @lai1979]—gives an example of how the sequential experimental design can play a role in an active learning procedure. In particular, [@Lai1982] shows that the LSE for linear regression models with adaptive designs has some nice asymptotic properties under rather general design conditions, as follows.

-   [(A2)]{} The random error $\{\epsilon_n\}$ is 