Lesson 8 Properties of Least-squares Estimators

Summary

The purpose of this lesson is to apply results from Lessons 6 and 7 to least-squares estimators. First, small-sample properties are studied; then consistency is studied.

Generally, it is very difficult to establish small- or large-sample properties for least-squares estimators, except in the very special case when H(k) and V(k) are statistically independent. While this condition is satisfied in the application of identifying an impulse response, it is violated in the important application of identifying the coefficients in a finite-difference equation.

We also point out that many large-sample properties of LSEs are determined by establishing that the LSE is equivalent to another estimator ...

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