1 Introduction to the Power-Divergence Statistic. - 1. 1 A Unified Approach to Model Testing. - 1. 2 The Power-Divergence Statistic. - 1. 3 Outline of the Chapters. - 2 Defining and Testing Models: Concepts and Examples. - 2. 1 Modeling Discrete Multivariate Data. - 2. 2 Testing the Fit of a Model. - 2. 3 An Example: Time Passage and Memory Recall. - 2. 4 Applying the Power-Divergence Statistic. - 2. 5 Power-Divergence Measures in Visual Perception. - 3 Modeling Cross-Classified Categorical Data. - 3. 1 Association Models and Contingency Tables. - 3. 2 Two-Dimensional Tables: Independence and Homogeneity. - 3. 3 Loglinear Models for Two and Three Dimensions. - 3. 4 Parameter Estimation Methods: Minimum Distance Estimation. - 3. 5 Model Generation: A Characterization of the Loglinear Linear and Other Models through Minimum Distance Estimation. - 3. 6 Model Selection and Testing Strategy for Loglinear Models. - 4 Testing the Models: Large-Sample Results. - 4. 1 Significance Levels under the Classical (Fixed-Cells) Assumptions. - 4. 2 Efficiency under the Classical (Fixed-Cells) Assumptions. - 4. 3 Significance Levels and Efficiency under Sparseness Assumptions. - 4. 4 A Summary Comparison of the Power-Divergence Family Members. - 4. 5 Which Test Statistic?. - 5 Improving the Accuracy of Tests with Small Sample Size. - 5. 1 Improved Accuracy through More Accurate Moments. - 5. 2 A Second-Order Correction Term Applied Directly to the Asymptotic Distribution. - 5. 3 Four Approximations to the Exact Significance Level: How Do They Compare?. - 5. 4 Exact Power Comparisons. - 5. 5 Which Test Statistic?. - 6 Comparing the Sensitivity of the Test Statistics. - 6. 1 Relative Deviations between Observed and Expected Cell Frequencies. - 6. 2 Minimum Magnitude of the Power-Divergence Test Statistic. - 6. 3 Further Insights into the Accuracy of Large-Sample Approximations. - 6. 4 Three Illustrations. - 6. 5 Transforming for Closer Asymptotic Approximations in Contingency Tables with Some Small Expected Cell Frequencies. - 6. 6 A Geometric Interpretation of the Power-Divergence Statistic. - 6. 7 Which Test Statistic?. - 7 Links with Other Test Statistics and Measures of Divergence. - 7. 1 Test Statistics Based on Quantiles and Spacings. - 7. 2 A Continuous Analogue to the Discrete Test Statistic. - 7. 3 Comparisons of Discrete and Continuous Test Statistics. - 7. 4 Diversity and Divergence Measures from Information Theory. - 8 Future Directions. - 8. 1 Hypothesis Testing and Parameter Estimation under Sparseness Assumptions. - 8. 2 The Parameter ? as a Transformation. - 8. 3 A Generalization of Akaike's Information Criterion. - 8. 4 The Power-Divergence Statistic as a Measure of Loss and a Criterion for General Parameter Estimation. - 8. 5 Generalizing the Multinomial Distribution. - Historical Perspective: Pearson's X2 and the Loglikelihood Ratio Statistic G2. - 1. Small-Sample Comparisons of X2 and G2 under the Classical (Fixed-Cells) Assumptions. - 2. Comparing X2 and G2 under Sparseness Assumptions. - 3. Efficiency Comparisons. - 4. Modified Assumptions and Their Impact. - Appendix: Proofs of Important Results. - A1. Some Results on Rao Second-Order Efficiency and Hodges-Lehmann Deficiency (Section 3. 4). - A2. Characterization of the Generalized Minimum Power-Divergence Estimate (Section 3. 5). - A3. Characterization of the Lancaster-Additive Model (Section 3. 5). - A4. Proof of Results (i) (ii) and (iii) (Section 4. 1). - A5. Statement of Birch's Regularity Conditions and Proof that the Minimum Power-Divergence Estimator Is BAN (Section 4. 1). - A6. Proof of Results (i*) (ii*) and (iii*) (Section 4. 1). - A7. The Power-DivergenceGeneralization of the Chernoff-Lehmann Statistic: An Outline (Section 4. 1). - A8. Derivation of the Asymptotic Noncentral Chi-Squared Distribution for the Power-Divergence Statistic under Local Alternative Models (Section 4. 2). - A9. Derivation of the Mean and Variance of the Power-Divergence Statistic for ? > -1 under a Nonlocal Alternative Model (Section 4. 2). - A10. Proof of the Asymptotic Normality of the Power-Divergence Statistic under Sparseness Assumptions (Section 4. 3). - A12. Derivation of the Second-Order Terms for the Distribution Function of the Power-Divergence Statistic under the Classical (Fixed-Cells) Assumptions (Section 5. 2). - A13. Derivation of the Minimum Asymptotic Value of the Power-Divergence Statistic (Section 6. 2). - A14. Limiting Form of the Power-Divergence Statistic as the Parameter ? ? ? (Section 6. 2). - Author Index. Language: English