Convergence

Convergence is a process in statistical analysis describing a series of calculations or guesses for the purpose of ultimately producing a very precise estimate. A simple example of several related equations illustrates the process. Imagine being tasked with solving the following set of equations for X and Y:

$$X+Y=5,$$

$$X-Y=3,$$

$$2X+3Y=12.$$

Given only Equations 1 and 2, the task easily yields X = 4 and Y = 1. However, these values do not satisfy Equation 3, for which substituting X = 4 and Y = 1 would yield 11 rather than 12. In fact, there is no exact solution for X and Y that satisfies all three equations. Still, one may wish to know what estimates of X and Y, $\tilde{X}$ and Ỹ, respectively, make all three equations as ...