Note on optimizing weights for multiple regression of remote sensing data

Abstract

For the high accuracy estimation of rice yield, multiple linear regression is suitable using remote sensing data by weighting data, and the weights may differ between current year and past years. In addition, the weights of past years may vary somewhat. A probabilistic optimization method is attempted to optimize weights. Multiple linear equation is used as regression equation. The result shows that as far as the data at hand is concerned, the different weights for past years data augment predictive error. The same weight for current year data and past years’ data gives the minimum predictive error. This is a typical example of deteriorating predictability by over-fitting responsible for over-parameterization. However, a shrinkage method for the optimal weights can make the predictive error smaller than that given by equal weights.