## LSU Historical Dissertations and Theses

1989

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Renewable Natural Resources

Quang V. Cao

#### Abstract

Different parameter estimation methods of yield prediction models were investigated using data from the Southwide Loblolly Pine Seed Source Study. This project consisted of three distinct studies. Each study dealt with a possible situation in which other parameter estimation methods rather than the ordinary least squares (OLS) estimator might be used. Three different evaluation statistics were computed to select the "best" estimation method for each situation. The objective of the first study was to select the best estimator for a yield model which had multicollinearity among independent variables. Three types of biased estimators were compared with the ordinary least squares estimator in terms of the predictive ability of the yield model. Ridge estimators were better than the OLS estimator in dealing with multicollinearity problems. Among methods used for selecting the ridge parameter k, Mallows's (1973) C$\sb{\rm k}$ statistic provided the best ridge estimator. On the other hand, principal components and Stein-rule estimators performed poorly compared to the OLS estimator in prediction problems. However, the improvement of yield prediction by ridge estimator was not enough in terms of volume per acre. Thus, the OLS estimator might be preferable due to the simplicity. The second study dealt with the calibration of yield prediction models to a specific locality and seed source by using Stein-rule estimators. The Stein-rule estimators provided better yield prediction for a specific locality than OLS estimators. For seed sources, however, the Stein-rule estimators offered little gain in prediction compared with the OLS estimators. In the third study, Kalman filter estimators were used to update yield prediction models by combining OLS estimators from the sample data with some prior information. Two different sources of prior information were applied in this study. Kalman filter estimators performed better in both cases than OLS estimators. Kalman filter estimators also predicted yield better when prior information was obtained from inside the study area than from outside of the study area.

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