Goodness-of-Fit Statistics for Discrete Multivariate Data

摘要: 1 Introduction to the Power-Divergence Statistic.- 1.1 A Unified Approach Model Testing.- 1.2 The 1.3 Outline of Chapters.- 2 Defining and Testing Models: Concepts Examples.- 2.1 Modeling Discrete Multivariate Data.- 2.2 Fit a Model.- 2.3 An Example: Time Passage Memory Recall.- 2.4 Applying 2.5 Measures in Visual Perception.- 3 Cross-Classified Categorical 3.1 Association Models Contingency Tables.- 3.2 Two-Dimensional Tables: Independence Homogeneity.- 3.3 Loglinear for Two Three Dimensions.- 3.4 Parameter Estimation Methods: Minimum Distance Estimation.- 3.5 Generation: Characterization Loglinear, Linear, Other through 3.6 Selection Strategy Models.- 4 Large-Sample Results.- 4.1 Significance Levels under Classical (Fixed-Cells) Assumptions.- 4.2 Efficiency 4.3 Sparseness 4.4 Summary Comparison Family Members.- 4.5 Which Test Statistic?.- 5 Improving Accuracy Tests with Small Sample Size.- 5.1 Improved More Accurate Moments.- 5.2 Second-Order Correction Term Applied Directly Asymptotic Distribution.- 5.3 Four Approximations Exact Level: How Do They Compare?.- 5.4 Power Comparisons.- 5.5 6 Comparing Sensitivity Statistics.- 6.1 Relative Deviations between Observed Expected Cell Frequencies.- 6.2 Magnitude 6.3 Further Insights into Approximations.- 6.4 Illustrations.- 6.5 Transforming Closer Tables Some 6.6 Geometric Interpretation 6.7 7 Links Statistics Divergence.- 7.1 Based on Quantiles Spacings.- 7.2 Continuous Analogue 7.3 Comparisons 7.4 Diversity Divergence from Information Theory.- 8 Future Directions.- 8.1 Hypothesis 8.2 ? as Transformation.- 8.3 Generalization Akaike's Criterion.- 8.4 Statistic Measure Loss Criterion General 8.5 Generalizing Multinomial Historical Perspective: Pearson's X2 Loglikelihood Ratio G2.- 1. Small-Sample G2 2. 3. 4. Modified Assumptions Their Impact.- Appendix: Proofs Important A1. Results Rao Hodges-Lehmann Deficiency (Section 3.4).- A2. Generalized Estimate 3.5).- A3. Lancaster-Additive A4. Proof (i), (ii), (iii) 4.1).- A5. Statement Birch's Regularity Conditions that Estimator Is BAN A6. (i*), (ii*), (iii*) A7. Chernoff-Lehmann Statistic: A8. Derivation Noncentral Chi-Squared Distribution Local Alternative 4.2).- A9. Mean Variance > -1 Nonlocal A10. Normality 4.3).- A12. Terms Function 5.2).- A13. Value 6.2).- A14. Limiting Form +- Author Index.