The benefit of a linear estimator is it is a lot easier (both computationally and algorithmically) to fit/solve a linear model than a non-linear model. Thus, there are advantages to linear models. Further, despite it being called linear, the model can actually be quite complex. It only needs to be linear in the model coefficients, but the regressors/independent variables don't have to be linear. Thus, you can make one variable the square of another variable or add a variable that is the interaction of two other variables. By doing so, you can add non-linearity while still using linear methods to solve the equation.
Ok, so then once you see the value of a linear model, then the next question is why we would want the best and most unbiased. I think those are rather obvious.
> The next question is why we would want the best and most unbiased. I think those are rather obvious.
It's not obvious to me why we want an unbiased estimator actually. A Maximum-Likelihood estimate, for example, seems just as reasonable. Do you have an explanation?
Not just that, but there's also the question of why we're looking for point estimates in the first place. It isn't the correct thing to do, but no one ever gives an explanation.
The benefit of a linear estimator is it is a lot easier (both computationally and algorithmically) to fit/solve a linear model than a non-linear model. Thus, there are advantages to linear models. Further, despite it being called linear, the model can actually be quite complex. It only needs to be linear in the model coefficients, but the regressors/independent variables don't have to be linear. Thus, you can make one variable the square of another variable or add a variable that is the interaction of two other variables. By doing so, you can add non-linearity while still using linear methods to solve the equation.
Ok, so then once you see the value of a linear model, then the next question is why we would want the best and most unbiased. I think those are rather obvious.