OK - so given some universe of bonds, that may be a superset of the index members, you are looking for a set of portfolio weights (many of which presumably zero) so as to minimize some measure of tracking error to the index, subject to some constraints related to liquidity, position size, etc. From a high level, you can go in a couple of very different directions here. The almost model free one would be to try to have your portfolio match the index on things like ratings, OAS, industry and maturity. If a large portfolio is feasible, then this is likely to be pretty robust, but not very precise. The smaller the portfolio, the harder it will be to find the right bonds to match the index. The more quanty approach would be to estimate a set of key rate interest rate durations and some kind of credit quality scaled spread durations, and create a portfolio that closely matches the index on these metrics. Down this path you will encounter, if not dragons, at least plenty of estimation problems. One annoying fact that eliminates many of the statistical techniques relied on by equity people is that you have to be able to deal with new securities on a very regular basis, and the old ones keep on changing their nature (in particular their maturity and OAS).