Comparison of regression techniques for certain patterned matrices in the errors in variables model

The goal of this research is to study and overcome a severe collinearity problem in the satellite data. Future satellites will have more than 2000 predictors. Those predictors are severely collinear. In this research, which method among ridge, principal component and ordinary least square regression would be a simple and robust approach to these kind of problems will be found using both theoretical and heuristic arguments. The closed form of prediction of Y is derived for several Fs which show the linear dependency structure of predictors. Simulation studies assuming a possible linear dependency structure are performed. The relationship of ridge and principal component regression (PCR) is investigated for the case of severe collinearity with measurement errors when a possible linear dependency structure is assumed. Comparison of the sum of squared error (SSE) between PCR and ridge regression is shown, and the range of k that SSER < SSEP for this special case is found. Several analytical results for this case are revealed. An application to the data from the NOAA-K is analysed with three different regression techniques.