Using PEOX IML for iteratively re-weighted multiple linear regression with a block-diagonal covariance matrix.

摘要

We have been using PROC IML to model the magnitude of a seismic event using signals from one to four seismic stations. Geological properties of the earth through which the shock waves travel introduce a correlation between the recorded signals for each event. Thus up to four correlated dependent variables are recorded for each value of the independent variable. We estimate the dependence of the measured seismic signals on the source using weighted linear regression with a block-diagonal covariance matrix in which the blocks are not all the same dimension and the covariances need to be estimated. After several iterations the weights and covariances converge. We can then estimate the magnitude of the source using a weighted average of the seismic signals, in which the weights and the variance of the estimate depend on which subset of the stations recorded the signal. PROC IML is a useful and succinct programming tool for this problem.