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| Preface | |
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| Statistical Spaces | |
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| Basic Properties of Statistical Spaces | |
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| Measure in Statistical Spaces | |
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| Equivalence and Divisibility of Family of Probability Distributions | |
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| Conditional Probability and Sufficient Statistics | |
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| Statistics and Random Variables | |
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| Conditional Probability | |
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| Sufficient Statistics | |
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| Exponential Family and Completeness | |
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| Exponential Family | |
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| Completeness | |
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| Sufficiency and Completeness | |
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| Ancillary Statistics | |
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| Estimation Methods Based on Statistical Space | |
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| Moment Estimation and Median Estimation | |
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| Maximum Likelihood Estimators | |
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| Quality of Estimators | |
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| Comparison of Estimators | |
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| Nonparametric MLE for Population cdf | |
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| Problems | |
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| Methods of Statistical Tests | |
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| Introduction: Background of Problem | |
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| Likelihood Ratio Tests | |
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| The Likelihood Ratio Methods | |
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| LRT's Limiting Distribution | |
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| Tests of Goodness-of-fit | |
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| Limiting Distribution | |
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| Test of Independence in Two-Way Contingency Table | |
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| Test of Independence in Three-Way Contingency Table | |
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| Goodness-of-Fit Test of Distribution Function | |
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| Sign Tests and Rank Tests | |
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| Sign Tests | |
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| Wilcoxon Signed Rank Tests | |
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| Wilcoxon Rank Tests | |
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| U-I Tests | |
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| Empirical Likelihood-Ratio Tests | |
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| Problems | |
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| The Comparison of Test Statistics | |
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| Probability of Two Types of Error in Hypothesis Test | |
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| Neyman-Pearson Fundamental Lemma | |
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| Unbiased Test | |
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| Comparing Power Functions | |
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| Test Procedures | |
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| Power Functions and Their Comparison | |
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| Comparing Robustness | |
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| Efficiency of Tests | |
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| Asymptotic Relative Efficiency | |
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| Interval Estimation Based on Test | |
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| Interval Estimation and Acceptance Region | |
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| Uniformly Most Accurate Confidence Interval | |
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| Uniformly Most Accurate Unbiased Confidence Interval | |
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| Uniformly Most Accuracy and Interval Length | |
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| Problems | |
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| Parametric Tests for Simple Models | |
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| One-Factor Model: Analysis of Variance | |
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| One-Factor Model: Multiple Comparisons | |
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| Multiple Comparisons | |
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| Generalized Multiple Comparisons | |
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| The False Discovery Rate Procedure | |
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| One-Factor Model: Trend Tests | |
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| Linearity Tests | |
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| Likelihood Ratio Test | |
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| Linear Rank Tests | |
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| Multi-Factor Model: Analysis of Variance | |
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| Model Without Interaction Effects | |
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| Model with Interaction Effects | |
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| Multi-Factor Model: Log-linear Models | |
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| Two-Dimensional Contingency Table | |
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| Three-Dimensional Contingency Table | |
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| Ancillary Parameter Model | |
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| Problems | |
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| Parametric Tests for Regression Models | |
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| Linear Models | |
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| Establishment of Model | |
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| Estimating and Testing the Parameters | |
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| Centralization | |
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| Regression Models | |
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| Regression Model and Linear Model | |
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| Errors-in-Variables Model | |
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| Logistic Regression Models | |
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| One-Variable Case | |
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| Multivariable Case | |
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| Time Series: Trend Term Models | |
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| Time Series: Autoregressive Models | |
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| Random Walk and Brownian Motion | |
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| Autoregressive Model | |
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| Granger Causality Tests | |
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| Granger Causality | |
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| Integration of Order d | |
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| Real Data Analysis | |
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| Problems | |
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| Bibliography | |
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| Index | |