Goodness-of-Fit Statistics for Discrete Multivariate Data [1 ed.] 038796682X, 9780387966823

Table of contents :
Title Page......Page img001_2R.djvu
Copyright Page......Page img002_1L.djvu
Preface......Page img003_2R.djvu
Contents......Page img004_2R.djvu
1.1. A Unified Approach to Model Testing ......Page img006_2R.djvu
1.2. The Power-Divergence Statistic ......Page img007_1L.djvu
1.3. Outline of the Chapters ......Page img007_2R.djvu
2.1. Modeling Discrete Multivariate Data ......Page img008_2R.djvu
2.2. Testing the Fit of a Model ......Page img010_2R.djvu
2.3. An Example: Time Passage and Memory Recall ......Page img012_1L.djvu
2.4. Applying the Power-Divergence Statistic ......Page img013_1L.djvu
2.5. Power-Divergence Measures in Visual Perception ......Page img014_2R.djvu
3.1. Association Models and Contingency Tables ......Page img015_2R.djvu
3.2. Two-Dimensional Tables: Independence and Homogeneity ......Page img016_1L.djvu
3.3. Loglinear Models for Two and Three Dimensions ......Page img018_2R.djvu
3.4. Parameter Estimation Methods: Minimum Distance Estimation ......Page img020_1L.djvu
3.5. Model Generation: A Characterization of the Loglinear, Linear, and Other Models through Minimum Distance Estimation ......Page img023_1L.djvu
3.6. Model Selection and Testing Strategy for Loglinear Models ......Page img026_1L.djvu
CHAPTER 4 Testing the Models: Large-Sample Results ......Page img028_1L.djvu
4.1. Significance Levels under the Classical (Fixed-Cells) Assumptions ......Page img028_2R.djvu
4.2. Efficiency under the Classical (Fixed-Cells) Assumptions ......Page img032_2R.djvu
4.3. Significance Levels and Efficiency unde rSparseness Assumptions ......Page img034_2R.djvu
4.4. A Summary Comparison of the Power-Divergence Family Members ......Page img037_1L.djvu
4.5. Which Test Statistic? ......Page img037_2R.djvu
5.1. Improved Accuracy through More Accurate Moments ......Page img038_1L.djvu
5.2. A Second-Order Correction Term Applied Directly to the Asymptotic Distribution ......Page img040_1L.djvu
5.3. Four Approximations to the Exact Significance Level: How Do They Compare? ......Page img040_2R.djvu
5.4. Exact Power Comparisons ......Page img044_1L.djvu
5.5. Which Test Statistic? ......Page img045_2R.djvu
6.1. Relative Deviations between Observed and ......Page img046_2R.djvu
6.2. Minimum Magnitude of the Power-Divergence Test Statistic ......Page img047_2R.djvu
6.3. Further Insights into the Accuracy of Large-Sample Approximations ......Page img049_1L.djvu
6.4. Three Illustrations ......Page img050_1L.djvu
6.5. Transforming for Closer Asymptotic Approximations in Contingency Tables withSome Small Expected Cell Frequencies ......Page img052_1L.djvu
6.6. A Geometric Interpretation of the Power-Divergence Statistic ......Page img053_1L.djvu
6.7. Which Test Statistic? ......Page img054_1L.djvu
CHAPTER 7 Links with Other Test Statistics and Measures of Divergence ......Page img055_1L.djvu
7.1. Test Statistics Based on Quantiles and Spacings ......Page img055_2R.djvu
7.2. A Continuous Analogue to the Discrete Test Statistic ......Page img057_2R.djvu
7.3. Comparisons of Discrete and Continuous Test Statistics ......Page img058_2R.djvu
7.4. Diversity and Divergence Measures from Information Theory ......Page img059_1L.djvu
8.1. Hypothesis Testing and Parameter Estimation ......Page img063_1L.djvu
8.2. The Parameter lambda as a Transformation ......Page img065_1L.djvu
8.3. A Generalization of Akaike's Information Criterion ......Page img068_1L.djvu
8.4. The Power-Divergence Statistic as aMeasure of Loss and a Criterion for General Parameter Estimation ......Page img070_1L.djvu
8.5. Generalizing the Multinomial Distribution ......Page img072_1L.djvu
Historical Perspective: Pearson's X2 and the Loglikelihood Ratio Statistic G2 ......Page img072_2R.djvu
1. Small-Sample Comparisons of X2 and G2 under the Classical (Fixed-Cells) Assumptions ......Page img073_1L.djvu
2. Comparing X2 and G2 under Sparseness Assumptions ......Page img076_1L.djvu
3. Efficiency Comparisons ......Page img078_1L.djvu
4. Modified Assumptions and Their Impact ......Page img081_1L.djvu
Appendix: Proofs of Important Results ......Page img083_1L.djvu
Bibliography ......Page img098_2R.djvu
Author Index ......Page img105_2R.djvu
Subject Index ......Page img108_2R.djvu

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