Sure, but even you have referenced Shadowstats...
Shadow stats is John Williams subscription sight. His numbers come from a simple adjustment to the government figure. He doesn't actually go back and recompute the inflation rate using the old method. The validity of the adjustment he makes has been questioned. He has offered a defense of it on his site. Intuitively, it seems the actual inflation we experience in our everyday lives is greater than the official inflation rate, and it always seemed to me that the Shadowstats figure was closer to the actual inflation I personally was experiencing.
http://www.shadowstats.com/ Williams has the current CPI at a touch over 4%, which seems about right to me.
From the economists' viewpoint, there are arguments that can be made in favor of hedonics. They don't seem, however, to apply to real life on this planet as we know it. It doesn't take a rocket scientist to realize why the use of hedonics is so attractive to politicians; it hugely reduces entitlement payments that are indexed to inflation saving billions upon billions of dollars.That takes the pressure off politically unpopular calls for payroll tax increases.
I prefer the old pre-1980s method of estimating the inflation rate. The new method essentially sweeps the inflation-created problem for entitlements under the rug and puts off the day of reckoning. We would be better off, in my opinion to make timely adjustments to entitlement contribution rates, but politics gets in the way. You can't get elected in this country by biting the hand that feeds you,i.e., cutting corporate welfare. Corporations fund political campaigns. And you can't get elected if you tell someone you're going to raise their payroll taxes. Hence hedonics, dreamed up by economists, came to the politicians' rescue. By underestimating the practical inflation rate you can, in effect, shave a little off of entitlements and transfer the proceeds, indirectly of course, to your big donors via 'enhanced', cost-plus government contracts, or special interest tax breaks. And the average guy on the street hasn't a clue. If we can ever change the way we fund political campaigns we might be able to solve this problem.
An example of the impact of the new inflation numbers versus the old, one can look at college tuition. I did this awhile back for my local University and provided the data to them. We all know that nominal tuition at public universities has "skyrocketed", and yet the schools without huge endowments are squeezed. So something is not right here. I used BLS and Dept. of Education figures and State budgets to explore this phenomena in an attempt to understand it. If you use the governments mean inflation figure and compound its effect over time, you'll get a result that tells you nominal tuition has gone up much more than it should have. But if you alter that inflation rate to 5%, the mean Williams rate over that time, you come out right on the nose. If the 5% Williams figure is much nearer actual inflation experienced by universities than is the ~2% government figure, tuition in constant dollars hasn't gone up at all, its held steady!
But universities are worse off today than they were 30 years ago, even after increases in tuition. How could that be? What I discovered is that, during that same 30 year period, public subsidies of higher education, in constant dollars (using the 5% figure), decreased on average by almost 30%! If that Williams inflation figure is real, than it would be no wonder that public universities are strapped for cash. The whole issue boils down to what inflation rate you use, and a 3% difference, when compounded over all those years makes a huge difference. I posted partial results of this study here on ET a couple years ago.