L17.4 Remarks on the LLMS Solution and on the Error Variance
Now that we have found the solution to the linear least mean squares estimation problem, it is time to offer a few comments, make some observations, and provide some insights. A first important observation is the following. In order to implement this estimator, you do not really need to know everything about the distribution of X and Theta. The only thing that you need to know is the mean of the two random variables that are involved, the variance of X, and the covariance of Theta with X. So it's only a few pieces of information that we need, and that means that we do not need to be so careful about modeling in a particular problem, as long as we know what the means, variances, and covariances are. This is a very desirable property, because it tells us that this could be simpler to implement in the real world. Now let us start looking at the form of the solution, and let's try to give some interpretation. Suppose that the correlation coefficient is positive. Then ...