The knowledge of channel statistics can be very helpful in making sound opportunistic spectrum access decisions. It is therefore desirable to be able to efficiently and accurately estimate channel statistics. In this paper we study the problem of optimally placing sensing times over a time window so as to get the best estimate on the parameters of an on-off renewal channel. We are particularly interested in a sparse sensing regime with a small number of samples relative to the time window size. Using Fisher information as a measure, we analytically derive the best and worst sensing sequences under a sparsity condition. We also present a way to derive the best/worst sequences without this condition using a dynamic programming approach. In both cases the worst turns out to be the uniform sensing sequence, where sensing times are evenly spaced within the window. With these results we argue that without a priori knowledge, a robust sensing strategy should be a randomized strategy. We then compare different random schemes using a family of distributions generated by the circular $\beta$ ensemble, and propose an adaptive sensing scheme to effectively track time-varying channel parameters. We further discuss the applicability of compressive sensing for this problem.