Define the GLS Estimator and Discuss Its Properties When $\Omega$ Is Known Why Is This Estimator Sometimes Called Infeasible GLS? What

question 32

Essay

Define the GLS estimator and discuss its properties when $\Omega$ is known. Why is this estimator sometimes called infeasible GLS? What happens when $\Omega$ is unknown? What would the $\Omega$ matrix look like for the case of independent sampling with heteroskedastic errors, where $\operatorname { var } \left( u _ { i } \mid X _ { i } \right) = \operatorname { ch } \left( X _ { i } \right) = \sigma ^ { 2 } X _ { 1 i } ^ { 2 } ?$
Since the inverse of the error variancecovariance matrix is needed to compute the GLS estimator, find $\Omega ^ { - 1 }$ . The textbook shows that the original model $\mathbf { Y } = \mathbf { X } \beta + \mathbf { U }$
will be transformed into $\tilde { \boldsymbol { Y } } = \tilde { \boldsymbol { X } } \boldsymbol { \beta } + \tilde { \boldsymbol { U } }$ where $\tilde { \boldsymbol { Y } } = \boldsymbol { F } \boldsymbol { Y } , \tilde { \boldsymbol { X } } = \boldsymbol { F } \boldsymbol { X } \text {, and } \tilde { \boldsymbol { U } } = \boldsymbol { F } \boldsymbol { U } \text {, and } \boldsymbol { \boldsymbol { F } ^ { \prime } \boldsymbol { F } } = \boldsymbol { \Omega } ^ { -1 }$
Find $F$ in the above case, and describe what effect the transformation has on the original data.

Recognize conditions and injuries associated with joint movement and ligament damage.

Explain the contributions of lifestyle choices to joint health and mobility.

Understand different types of easements and their implications for property rights and management.

Recognize various forms of property ownership and understand the legal rights and obligations associated with each.

---

Definitions:

Months

Units of time, each roughly equivalent to one twelfth of a year, used in planning and organizing.

Rate Of Interest

The percentage of the principal that will be charged for a particular period of time, normally one year.

Interest

The charge for borrowing money or the return on deposited funds, typically expressed as a percentage rate over a period of time.

Simple Annual Interest Rate

The percentage of the principal amount that will be charged or earned as interest, calculated once per year without compounding.