A Comparative Study of Test Procedures used in Assessing the Forecasting Ability of Linear Models with Applications in Crop-Yield Data

        Linardis Apostolis
        Supervisor: I. Panaretos
 

        CHAPTER 1
        INTRODUCTION

        METHODS OF EVALUATION OF LINEAR MODELS

        2.0 Notation and Terminology

        2.1 Residual Mean Square Criterion

        2.2 Coefficient of Determination

        2.3 Adjusted Coefficient of Determination

        2.4 Coefficient of Multiple Correlation

        2.5 Selection of Regression Coefficients

            2.5.1 The Backward Elimination Procedure

            2.5.2 The Forward Selection Procedure

            2.5.3 The Stepwise Regression Procedure

        2.6 Ridge Regression

        2.7 Mallows C_p Statistic

        2.8 Hocking's S_p Criterion

        2.9 Cross Validation - Press Criterion

        2.10 Bootstrap

        2.11 Likelihood Ration Test (x² - Test)

        2.12 Akaike Information Criterion(AIC)

        2.13 Bayesian Information Criterion (BIC)

        2.14 Amemiya Prediction Criterion (PC)

        2.15 Hannan's Criterion (HC)

        2.16 Theil's Residual Variance Criterion (RVC)

        2.17 Parzen's Criterion for Autoregressive Transfer Functions

        2.18 Bayesian Model Choice

        GAMMA-RATIO DISTRIBUTION

        3.1 Estimation of Predictions

        3.2 Testing of the Predictability of a Linear Model

        3.3 Comparing the Predictability of Two Linear Models  

        APPLICATIONS OF THE TESTS THAT EVALUATE THE PREDICTABILITY OF A LINEAR MODEL AND THAT COMPARE THE PREDICTABILITY OF TWO LINEAR MODELS BASED ON

        THE x² AND THE CORRELATED GAMMA-RATIO DISTRIBUTIONS

            4.1.1 Application of x² and Correlated Gamma Ratio Test for the Indiana Crop-Yield Data

            4.1.2 Inference based on the x²-test for the Predictability of One Linear Model

            4.1.3 Inference based on the Correlated Gamma Ratio Test about the Predictability of Two

                    Competing Linear Models

            4.1.4 Comparison of the Conclusions of the Test Based on the Correlated Gamma-Ratio

                    Distribution with the Test Based on the Cross Validation Method and the R² and R²_adj  

                    Coefficients

        4.2 Another Application of the Tests Based on the x² and Correlated Gamma Ratio Distributions for 

             the Iowa Crop-Yield Data

        4.3 Simulation Study

            4.3.1 Testing the Predictability of a Linear Model Based on the x²-distribution

            4.3.2 Comparing the Predictability of Two Linear Models Based on the Correlated Gamma-Ratio 

                    Distribution