Examples

The lmt parameter file is in written in “eXtensible Markeup Language” (xml). For under- standing the examples you may want to get a jump start in xml file structure first. Don’t be scared. Even without any previous knowledge you’ll be able to understand the xml structure used for lmt in less then half an hour. Please consult the Internet to find suitable introduction into xml

Estimating a mean

Consider the linear model $$y=Xb+e$$ where $$y$$ is a vector of $$n$$ observations, $$X$$ is as single column matrix of $$1$$, $$e$$ is the residual and $$y\sim N(Xb,R)$$ where $$R$$ is a $$n \times n$$ co-variance matrix. The generalized least square solution for $$b$$ would be obtained from $$b=(X'R^{-1}X)^{-1}X'R^{-1}y$$. Note that in simple cases $$R=I\sigma_e^2$$, where $$I$$ is an $$n \times n$$ identity matrix, and estimating $$b$$ simplifies to $$b=(X'X)^{-1}X'y$$, which is equivalent to $$b=\frac{\sum_{i=1}^n y_i}{n}$$.